@spwolf Additions:
I sent a txt file of the registry to support, but now I
tried to install PA on my Surface Pro 7 with W11 and the problem is there too.
The same behavior, when I open PA, it is functional and registered, if for any file
I right-click and select e.g. wrap or unwrap, a registration request pops up immediately.
So it’s not a single computer problem. (This information as a second email also sent to support.)