I'm not in a place to judge you based on your participation in the contest because I also am doing very poorly with my own entry. To be fair that's mainly because I'm focusing a lot of my after-work efforts on programming projects, but eh, that also counts as procrastination even if it's productive.
But fella to fella:
There's no such thing as not being "cut out" to be a writer. Even if you procrastinate, even if you think you're bad at it, even if writing can feel daunting and you develop an avoidant relationship with it. The only people that aren't "cut out" for it are people who loathe the craft, plagiarize/use AI for their work, or see it as a chore rather than the art form that it is. If you're someone that likes storytelling and wants to put their own story onto the paper, then you're a writer, simple as.
Mental health struggles are frustrating, but everyone deals with them. It doesn't make you less of a creative to have to forego a project so you can better take care of yourself, and pretty much everyone here can understand that. This isn't some final class project you need to get an A on in order to pass; we're just hobbyists hanging out and having fun fun while improving our craft. Seriously, no one is actually having panic attacks over the SHAME pit or losing some Internet points (at least I hope not, that would be fucking embarrassing LOL).
CYS is an old site, and it isn't going away until the apocalypse comes (and even then it'll probably be sitting untouched on a dusty server long outliving the Internet). It'll be right where you remember it whenever you feel as if you're ready to come back. Or you can just read stories on here in the meantime if you don't want to cut ties altogether, and maybe ease into productivity by writing short stories on the forums or short, just-for-fun unpublished storygames. Just as you can hone your writing abilities, so can you hone your ability to organize projects for yourself and become "productive." That's a skill too! You are a writer even if you're still just feeling things out right now. Don't barricade yourself from the title! That's not fair to you.
But in any case, good luck with whatever you got going on at home. I hope things get better for you and that you return to write again. :)