The problem of "existential anxiety" only ever exists precisely in reference to religions and spiritualities, old and more recent.
It's inconceivable otherwise. — baker

Suffering (with a capital "S") is simply the label I give all this negative understanding (self-awareness). Bed bugs, diseases, emotional trauma, and cancer are often situational and contingent. That is to say, they happen under certain conditions, in certain spaces and times at certain probabilities. The likelihood of any situational negative experience is high on a daily basis. The ability to combine this into a category and label it "Suffering", is something our species is able to do. Negativity/Suffering is simply a universal for a diverse set of instances. The name or label, or even manner in which it is spoken (metaphorical, allegorical, mythological) is less relevant.

However, there is another form that you can put into the bucket- the "existential" kind. This one is felt most with the emotional feeling of boredom. It's the engine running but no clearly interesting goals. It's the baseline. It's the Pascal's "cannot sit still in an empty room" scenario. Most cultures, at least to any degree of writing, has written about it- chasing after "vanity", Buddhist notions of dissatisfaction- Dukkha, Gnostic and Platonic notions of a corrupted reality and ideal reality. It all revolves around these themes of a general existential dissatisfaction.

Other animals do indeed feel pains and are harmed, but don't have the contingent-thinking to know that "something could be different". Things happen to most other animals. They don't opine that it could have been something else. They don't have the ability to see the picture of the category of Suffering in general.

So here we are, animals that can see the big picture of Suffering. That can know that things could be different, but are currently not the ideal.

The fact that we exist is something over which we have no control, it precedes us. As such, we have no say over its meaning. — baker

Hence the need for antinatalism as an ethic.

To try to figure out why we exist or why life is worth living and to make this a matter of decision is like trying to choose one's parents. That is, it's irrational, it cannot be done. — baker

I didn't say this. That's something you asserted here for some reason, kind of an aside maybe. When I said this:

Rather, all these "goods" are not necessarily only "factual" or objective but rather normative. There is an agenda, at the cost of much suffering. But we must look at this and see what it is we are trying to do here and why we are insisting on doing it. That's why I suggested we should treat existence as a political committee would, putting a moratorium on it until we understand why we trudge forth, but do this analysis unflinchingly, without the poetic cliches. — schopenhauer1

I mean in general, the human project. What are we wanting people to "do" here? Why procreate more people here? When someone begins to answer this, the agenda reveals itself. Suffering considerations take a back seat.