This seems like a decent place for discussion, given that the Let's Talk About Character page has 133 comments.
I'm fairly certain that preference regarding self-inserts and author avatars varies from person to person. I myself am totally down with both so long as they're well-written and aren't shoved in the reader's face. As far as the "what works" question goes, I feel like that can be attributed to the shift in focus from characters known solely by their surface abilities (Kondraki is butterfly king with camera and saber! Bright swaps bodies and ook ook orangutan!) to exploration of inner motivations and more humanized renditions. Also the Foundation-verse itself is better-defined these days, I think.
I do have both a self-insert (Researcher Zyn Kiryu who is kinda undeveloped, save for her neurotic orderly/tidy/neatliness and ambition) and an author avatar (Doctor Mark Kiryu, who was a therapy specialist and the broliest of bros also he likes ninja costumes). People have mentioned that it is weird reading about a self-insert when you've interacted with the author before (cognitive dissonance, I believe, it was). I can understand that.
Quite frankly, when it comes to writing characters, I try to focus on putting just a little bit of myself into one trait or quirk so they seem that much more realistic, and letting the rest come as the story or article requires it. I do recall first joining the site and desperately wanting to write myself into the world, but that in itself wasn't enough inspiration to create a solid character. And it doesn't help if you get too attached to characters that are too much like you—I know I've had trouble writing flaws into Mark because I'm so fond of him, haha.
Again, it all depends. It's easier to make a new character if you've got an engaging plot lined up for them. My approach for introducing Mark Kiryu was pretty subtle: nameless mention in a tale, briefly named in a testing log, then some interview dialogue in SCP articles, and later his own tales. Zyn Kiryu's full name was never mentioned in any of my tales, come to think of it.
Test the waters. See what other people think. Like writing your characters, but not to the point where you can't take crit about them. Not sure how many people that works for, but that was how I happened to do it.
