BetterTouchTool version incompatible


A few days ago I got the notification my license expired, so I bought the lifetime-license. Now the Tool doesn't restart, I get a Window saying "BetterTouchTool version incompatible" (see screenshot). Even deleting everything related to the BetterTouchTool from my Macbook (MacBook Pro 13" 2017, 4 Thunderbolt-Ports, 3.1GHz i5, 8GB RAM, MacOS 10.15.5) and installing the newest version of BTT from the downloads-website didn't help.
After licensing it via the received email I get the Window "Neustart nicht möglich" (have a look at the screenshot) followed by the other one "...version incompatible".

Also a folder on my desktop is created called BetterTouchToolDebug with some documents.

I do not know, what else I could try and need some help please.