Are not "your thoughts" definitionally "the thoughts you experience"? So if others were all able to experience each others' thoughts, they would all experience them as their own thoughts, and so experience themselves (and each other) as a single collective mind.

It is true that I can only experience my own thoughts and not anyone else's.

And everyone claims that to be true for their own selves.

But what if the others are lying? — god must be atheist

And what if you are lying?

Are you suggesting that we may be experiencing other people's thoughts and therefore we cannot definitely state that "I think, therefore I am"? If that's the case, I'd say it depends on one's definition of I.
Even if you were experiencing other people's thoughts, there still must be an entity that is experiencing. A consciousness, not necessarily a physical body.

Maybe I misunderstand the point you are trying to make.

You got it right, dead on, what I am saying.

Any thought truly shared by more than one person, and experienced therefore, is possible, and I have no way of verifying whether that happens or not.

What if I am lying? I can only lie to you and to those who are not me. To myself I can't lie.

You seem to misunderstand the concept of sharing, in the context that I am expressing it in. The concept of having access to other's thoughts directly, on an experiential basis.

It's like sharing a towel. If only you are able to experience a towel, you could declare, "I experience the towel, and therefore I am." If more than one people experience the towel, and they feel each other's experience with the towel, then they know what the others feel. Not just know, but experience.

Is it their own experience, and their own only? No. So if Peter uses the towel, and Fred experiences the drying feature of the towel, Fred can't declare "I am using a towel, therefore I exist", because he is not getting dry, he is just feeling the experience of another. On the other hand, Fred can declare "I experience the towel", and that can be a verification of his own existence for himself.

This is what it is. The big problem, of course, is that nobody knows if other people can and do share experiences or not. This is for those, who can only experience their own experiences.

There’s a term for this. Empathy. It happens when one experiences the experiences of another. If one doesn’t experience the experiences of another as one’s own but believes one does, then the empathy is delusional; hence, in all instances of non-delusional empathy, we experience each other’s experiences. I guess some hereabout would then question, “How does one know?” which can be simply answered with, “through gut feeling that is then verified via the other’s reactions to one's gut-feeling-based actions, or else falsified via the same”.

Here’s my thing with Descartes’s cogito. How else would one go about evidencing that consciousness—the so called “I”—is not illusory? This since some philosophers make it a habit to claim that consciousness does not reference anything real, but is instead a reified notion.

Well, one of the options after looking down from a window and wondering if the people are automatons is that one could check it out in that moment. Run out on to the street and scare the crap out of one of your neighbors.
But Descartes did not do that.
He finished his bath and went to bed.

So if others were all able to experience each others' thoughts, they would all experience them as their own thoughts — Pfhorrest

in my model, it does not work that way. I believe you are thinking about verbal thoughts, which are even more problematic than non-verbal. In my model of thinking, the cognitive agent has mostly hierarchical, non-verbal linguistic structures that are framed and rooted in their own meaning of the experience as filtered/morphed by their personality filter. So, if another cognitive agent had access to, say, ‘thoughts’ in terms of the first non-verbal linguistic layer then their different personalities and historic experiences would evoke different historic meanings and access/qualia experiences so the two agents would not be “thinking” the same thing and their flow of consciousness would quickly diverge from each other so could not “experience themselves (and each other) as a single collective mind”. I’m very sure this would also be the case in the human brain model.