Usually what you describe is what they do. Someone “owns” the AUR package (and it’s not quite literally any random user IIRC - you have to be accepted as an AUR maintainer I think) and they then take on the responsibility to repackage it whenever the author (you) releases a new version. There is also a mechanism for users to flag the AUR package as out of date in case that maintainer misses a release, and if they abandon it (or even if folks just don’t like how they package it) someone else can package it, assuming someone else wants to.
Sometimes the AUR maintainer is the dev themselves. I can’t think of a good example currently, but I know I’ve seen it before.
I don’t know the process for how things end up in the official repos, but I would guess it’s similar to however any other distros identify software they want to officially package.