Quicksand Fans

Basically with the person sinking intentionally being a way for the reader to self insert?

I have no such stories. However, an excellent writing exercise is to take an existing story (or scene from somewhere) and convert it into the POV (or other circumstance) that you want. So long as you really do that conversion and properly recognize the original source, that ought to get you what you want and perhaps what others would like, I have done that sort of conversion myself on some of my own stories and found it useful.

A similar exercise might be to convert a scene you have watched first into a screenplay script and then into a short story (or the reverse). Note that in a screenplay the viewer is not inside any character' head, so things such as emotions must be acted by the performer, whereas the writer, and thereby the reader) IS inside the character's head.

There was a story called The Final Hope which I believe was first person and lacked indications of gender/sex. I don't recall the author. I faintly remember there being some second-person experiments in the stories section of this site, but I'm afraid I couldn't name them.

There is an old (2009) story on page 39 of the Stories section, “Summer of ‘76,” that I wrote under my previous handle here (jack c). It is written in first person and contains a short 1st-person segment of sinking along with a female friend. Not sure that it measures up to what you are looking for, but you might want to check it out.

I wrote a couple of stories waaaay back that had insert-yourself opportunities/ Posted over in the stories forum:
Riding Gear. 1st person male.
Quicksand Suicide. 1st person, non-specific
Mountain Quicksand. This swaps between first person from the observer's role and third person onmiscient.

Also, i did a series of videos in which you are the person sinking while your girlfriend/lover Marizel watches. There are 3 different scenarios:
https://stuck-in-paradise.umd.net/