Here we are, probably less than a month away from Big Sur shipping to Mac customers. I can say that there are significant bugs, especially affecting multi-monitor support that can affect your usage of CurrentKey Stats. https://developer.apple.com/forums/thread/651131?answerId=644269022
There was another Big Sur bug that caused CurrentKey to crash, but I’ve fixed that (in a new update to the app). Other Big Sur bugs however, I can’t really mitigate until they’re fixed in the OS itself.
So, I’d recommend if you want to keep using a stable version of CurrentKey Stats, to delay updating to Big Sur for the time being.
I will update this post if/when the Big Sur bugs get fixed.