For some reason, my vertices won’t snap on this specific file of my character.
My settings have not changed, not sure what is causing this.

Separate Objects? Then check your settings in the dropdown panel of the snap settings. Otherwise share the file.
Here is the file. It is one object, yes.
https://www.mediafire.com/file/sazdp6j5jylfocx/Wild+Between+Worlds.blend/file
The file crashes for me on load.
Same for me.
https://www.mediafire.com/file/amknexuiyn5b9h8/Wild+Between+Worlds.blend/file
Here, I disabled the plugins. Sorry about that.
Its still broken and there’s something really corrupt internally. I cant even append the objects of that file. I’d suggest to open a new blendfile and transfer the content soon if it still works for you.
Might even lead to a working selection state again if you did.
The mesh 0x01C3C8 is corrupted.
You can append all the other meshes except that one.
If you have it in a previous file (or backup session) try to use that.