For author self inserts, yes I do enjoy them sometimes…especially when it’s a more minor or side character that can break the 4th wall a little bit, for example to deliver some sage advice to the MC on their journey, make an inside joke, or deliver meta information to the player in a clever way. I find that kind of interesting, and some writers are fun to engage with in that way.
For a character that is in danger of possibly overshadowing the MC… what about just making that character the MC in that case? Or least incorporating some of that character’s backstory or other unique traits into the existing MC? I think I wouldn’t mind that if it was also a character I could play as and root for. I enjoy playing more set characters from time to time.
Personally, I admit I do find it fun to write short stories like this sometimes with self insert characters… I just don’t share them usually and keep them mostly for myself in my own journals. For the most part, I doubt anyone else would find them as cool or interesting as I do, lol. That’s kind of the problem with self insert characters I guess, they can be very personal.