I was noticing this problem on the release channel and then updated to the Alpha channel and the problem is still present. The only way I can regain use of my keyboard is by quitting better touch tool and restarting it.
I am on the Big Sur version 11.5.2 on a 2020 M1 MacBook air base model and BTT Version: 3.581 (1724)
Also, the app often appears last in the app switcher even if I was just creating more shortcuts and using it. I have auto hide set for my menu bar and when I have BetterTouchTool open when I'm building a shortcut or somesuch it often is impossible to get to my menu bar without clicking out of BetterTouchTool first. That is, when better touch tool is in focus it eliminates my ability to access the menu bar – very often.
These non-keyboard issues are nearly constant and do not seem to be remedied by restarting the app.