A central theme in those "manuals" is that passion clouds perception of what is going on. Both Marcus Aurelius and Epictetus struggled with those around them. The indifference that was proposed was done in the face of others who were invested in their demise or denigration. They are making a connection between courage and understanding.
Or put another way, the stoic response assumes the ever present influence of Strife.

They are making a connection between courage and understanding.
Or put another way, the stoic response assumes the ever present influence of Strife. — Valentinus

So, are you saying that courage and understanding are the proper responses towards Strife? How does one not indulge in too much indifference, then?

There is a Buddhist slant to the OP; but, lacking in compassion if one becomes indifferent towards 'desire' then one is left with apathy. Just a passing thought that I didn't want to mention in the OP; but, deserves mentioning nevertheless.

So, are you saying that courage and understanding are the proper responses towards Strife? How does one not indulge in too much indifference, then? — Wallows

I am not saying what is a proper response. That is your problem given only to you as it is given to me as my problem. We all have these peculiar assignments, given to each of us. Our attempts to sort these elements out either lead to some kind of policy for ourselves or not.

The courage part is accepting those conditions and not waiting for better ones.

"indifference" (the central theme of Stoicism) — Wallows

If “indifference” is the central theme of Stoicism, how could you explain that both Marcus Aurelius and Seneca were the most powerful people of their time, effectively ruling and governing the Roman Empire? Were they The Lame Stoics?

I think you gave an excellent example of Stoicism Well done.

If “indifference” is the central theme of Stoicism, how could you explain that both Marcus Aurelius and Seneca were the most powerful people of their time, effectively ruling and governing the Roman Empire? Were they The Lame Stoics? — Number2018

No, Seneca and Marcus Aurelius, we're not "Lame Stoics", however, Epictetus literally was. I speak of just the "apatheia", characteristic of Stocism, which is actually encouraged by the Stoics. What are your thoughts about that?

No, Seneca and Marcus Aurelius, we're not "Lame Stoics", however, Epictetus literally was. I speak of just the "apatheia", characteristic of Stocism, which is actually encouraged by the Stoics. — Wallows

As far as I know, even Epictetus encouraged his pupils to be actively engaged in the
“outer” world. And, himself, as a spiritual leader and teacher, he did not dispose of his duties in his school. In general, one could claim that the central theme of Stoicism was not simple “indifference” and becoming “apathetic,” but also a passion of working on self, of indifference while being fully involved in the "external" events.

In general, one could claim, that the central theme of Stoicism was not simple “indifference” and becoming “apathetic,” but also a passion of working on self, of indifference while being fully involved in the "external" events. — Number2018

Yes, there has been a perversion of the term "apatheia" towards the modern day definition of "apathy". I guess I'm rebelling over this perversion here.

Anyway, "indifference" (the central theme of Stoicism) is a two-edged sword. — Wallows

I don't think "indifference" is the central theme in Stoicism. I think the central theme, if there is one, is understanding the difference between things in our control, and things beyond our control.

Clearly, no Stoic would say that we should be "indifferent" to things in our control (essentially, and stated simply, our thoughts, feelings and conduct). Things in our control are to be directed to virtue and living "in accordance with nature." Things outside of our control should not distract us from the pursuit of virtue; they should not be allowed to disturb us, provoke us, render us hateful or fearful, etc. We should therefore be "indifferent" to them in that sense. Being indifferent to them doesn't require apathy, though. We simply understand that they're beyond our control, and are not paramount in determining how we feel or think, or what we should do.

how do you strike a balance between the internal conflict dwelling within and the external day-to-day issues, sturm und drang, — Wallows

I was struck by the following fragment from Marcus Aurelius’ Meditations:
"always to define
whatever it is we perceive—to trace its outline—so we can
see what it really is: its substance. Stripped bare. As a
whole. Unmodified. And to call it by its name—the thing
itself and its components, to which it will eventually return.
Nothing is so conducive to spiritual growth as this capacity
for logical and accurate analysis of everything that happens
to us. To look at it in such a way that we understand what
need it fulfills, and in what kind of world. And its value to
that world as a whole and to man in particular—as a citizen
of that higher city, of which all other cities are mere
households.
What is it—this thing that now forces itself on my notice?
What is it made up of? How long was it designed to last?
And what qualities do I need to bring to bear on it—
tranquillity, courage, honesty, trustworthiness,
straightforwardness, independence or what?"
It includes the most important and interdependent themes of Stoicism
that one could apply nowadays – spiritual growth is impossible without logical
and accurate analyses of one’s habitual surrounding. Therefore, the endless accumulation of knowledge and concepts that have not applied to one’s life is meaningless. And, it poses a problem: how to call things by their names, what language should be used?

I think that you are right in defining the central theme of Stoicism. I just want to add
two more points about difficulties of practicing the stoic “indifference” today. First, after understanding what his true possession is, the Stoic had started practicing the indifference, and the main part was the ceaseless oral and mindful repetition of “handy” truths and maxims so that they had become his inner beliefs. How to differentiate such a practice from numerous auto training psychological recommendations? Second, there is an impossibility to find a clear border between “inner” and “outer,” an inner mind and an external world. How can we determine an authentic mine-ness? So many people cherish, strengthen, and cultivate their “I”; nevertheless ones have become more obeying the dominating outer norms.

I'm not sure I understand, but I don't think it's necessary to distinguish "inner" from "outer." It isn't clear to me that can be done, nor do I think it useful. It's possible, though, to distinguish what I think, feel and do as a part of the world from other parts of the world. We interact with others and with the rest of the world constantly; we don't live apart from the world. But, we each have the ability to not merely react to the rest of the world, but to interact with it intelligently. Understanding what is in our control and what is beyond our control is the first step, or one of the first steps, in living reasonably.

But, what if I said that the Buddha was right, and desire is the origin of suffering? Then should we be indifferent towards this 'inner conflict' that resides within us? And, why can't you draw a line between what is inner and outer?

It's possible, though, to distinguish what I think, feel and do as a part of the world from other parts of the world. — Ciceronianus the White

Sorry for being vague. I tried to point out that quite often what I think, feel, and percept has indeed been induced and enforced by external socio-cultural forces; and, in most cases, I do not recognize it. Further, under these circumstances, it can be challenging to practice Stoicism in its classical form. I may think that the most intimate parts of myself are under my control, but actually, they are not.

I think a Stoic would say that desire related to things beyond out control leads to suffering. I don't know if that's what Buddha meant. And, I'm not sure what you refer to as "the inner conflict."

I personally don't feel that there is some "me" which exists apart from the rest of the world. I'm a living organism which has certain characteristics living in an environment.

Because we're part of the world, we necessarily interact with other parts of the world. There's no denying that. But we have a certain, albeit limited, ability to govern ourselves, and how we interact. We can think, in other words. We can make judgments and assess the consequences of judgments. We can discipline ourselves. From the Stoic perspective, that's what it is to live in accordance with reason, which is to live in accordance (so say the Stoics) with nature.

But, surely the Stoics were no machines. They must have had desires for things beyond their control. Therefore if one professes an attitude of apatheia, then let it be for all things originating from desire. Including those things within our control. This is what I mean to say by 'inner conflict'.

I completely agree with your way of defining a classical stoic doctrine – you keep stating it (and, I think that this stoic truth worth being said again and again!)
Nevertheless, nowadays we encounter new realities that make practicing Stoicism almost impossible. When one watches a movie, plays a video game, works as a financial trader – she has minimal control over her thoughts, feelings, perceptions, etc. Further, most of the contemporary intensive working and stimulating
environments completely subjectivate individuals. They in-form them, imposing composite and inevitable Modi of being and thought. Therefore, today it is much more challenging to obtain autonomy and independence of mind than 2000 years ago.

Your argument goes something like this:

If one embraces stoicism, then one needs also to embrace the principle of “indifference” which can lead to becoming apathetic.
One should not embrace something that leads to them becoming apathetic.
Therefore, one should not embrace stoicism.

There are two crucial aspects of stoicism that you are overlooking. Both of my objections will be aimed at your conditional in premise 1, as I assert that your claim that embracing stoicism has the implication of apathy is a wrong one. Though becoming apathetic towards everything is a commonly expressed worry about the Stoic school of philosophy, it is only a worry if one malpractices stoicism and does not grip onto several of its most crucial claims. The first, and most important aspect of stoicism that I believe you are mislabeling is their principle of indifference. Stoics commonly get a wrap for being indifferent towards everything but that is not a claim well-supported by stoicism. Stoics have very distinct passions, only towards internal matters and not external. The reason they label externalities as indifferent is because they are not under the control of the stoic, any matter that does concern the stoic having complete control a stoic has a great deal of care for. Stoics care about living a virtuous life and doing their duty more than the majority of non-stoics. Apathy emerges from a disregard of all passion in life, the stoic’s mentality is not that they should disregard all passions in life, but rather, it is that they place a large importance on the right distribution of passions and expectations. They believe that negative feelings come from the gap that exists between expectations and reality, so by not holding any expectations about the outside world and only over things they control the stoic is only supposed to experience positive emotions. Thus, depression shouldn't be in the mix of true stoicism.
Also, especially going off of the stoic teachings of Epictetus, I think that you mislabel the stoic’s interaction with the outside world. A worry I hold with your version of the stoic’s principle of “indifference”, is that you frame the indifference as if the stoic’s not only do not hold expectations for the outside world, but also do not hold the outside world as being a source of pleasure in any sense. Epictetus’, a philosopher you refer to as being a model of stoicism for you, famous example of being at a feast frames the stoic’s relationship with the outside world in a different way. He asserts that it is okay to take from a plate that is being passed around at a feast and enjoy the food that is presented, as long as you take in moderation. The key that he points out is that the Stoic should not have any expectations for having a feast, the selection of the feast, who is present, or what the food is like. By not having any previous expectations of the outside world, the Stoic will not experience negative expectations that originate through the wrong placement of their interests. Nevertheless, the stoic is definitely allowed to enjoy the external things presented to them in Epictetus’ view, so this complete apathy to everything that you assert that stoicism entails I think is wrongly based. The stoic is supposed to not hold expectations of the outside world, but they may still have interests in the outside world as presented to them.
In conclusion, I assert that the first premise in your argument is misdirected. Apathy is not an implication of stoicism if stoicism is put into practice correctly. By still having passions towards the internal circumstances of themselves, and allowing themselves to receive pleasure from outside circumstances as long as they are not attached to the situation that this pleasure was derived in and did not hold expectations about it, the stoic does not experience the apathy that is your concern.