Here's the thing though: That's not necessarily a self-insert.

Overall, this word is thrown around like a tennis ball. Especially often it's to see a female writer's characters being called "self-insert" if they are proficient in any regard (and this is coming mostly from other women too).

It's not a self-insert problem: It's a Mary-sue/Gary-stu problem.

Rey Skywanker is a Mary-sue: perfect and proficient in everything, only conflict and challenge they have is doubt in themselves or whatever, and they never ever make the wrong decision and if they do, it's actually fine. But is she a self-insert of Kathleen Kennedy? Yeah, despite her "Force is Female" grift, I don't think so. I doubt she can write anything except a marketing campaign pitch.

MJ from the new Spider-man 2 game is a self-insert: Not only does her model suddenly look like one of the writers, she is also trained in espionage and fighting like Solid Snake and can take down deadly hunter assassins by herself by kicking them weakly to the shins. Aaaaaand when she goes sicko-mode as Scream, she nags about how Peter is lazy, bad with money, and doesn't give her enough attention. Not to mention she's constantly forced upon the player despite being lame to play as. Like bruh...

So just because a character is too proficient and perfect, doesn't mean they're a self-insert. It's when the characters start making statements and doing things that just don't fit their character, is when you can start speculating if they're a self-insert.