Hello, sorry about late response!
Normally I bookmark posts that I create asking for help, then check back daily.
Since this post went to moderator for approval, there was nothing to bookmark at that specific point, I waited for email confirmation post was accepted. Seems these are not sent out, and I guess life got in the way in between
In any case, I went through absolute hell and back but did manage to solve it!
Since this issue was only happening with Sigil (I could post custom characters in all other apps, including older versions of Sigil) I figured this would be a good place to start with the debugging.
In the end, the issue was with AutoHotKey. What I did was navigated to the install directory and set AutoHotkey.exe to run with administrator privileges. Problem solved!
I have no idea in the world why AHK lacking administrator privileges would have caused characters to not come up with Sigil 2.02 specifically (and no other apps) but I suppose that's a deeper mystery.
In any case, hopefully this thread can sit here as a google-able resource for anybody else who comes into this specific issue.
Thanks for all of your help and support, and once again, I'm sincerely sorry for missing all the comments!