One thing that many people have requested is notification icon badges for Toot!. The main reason they have not been implemented is that I've always found the use of notification badges a very toxic pattern to drive addictive behaviour on social media apps, always trying to nudge you back to opening the app.
I was thinking, though, that this mainly applies to things like favourites and other things that you don't REALLY need to know right now. So I was thinking enabling them for mentions only (and maybe some other things that require immediate attention like admin report notifications) might make sense. What do you think?