Thanks, I came right with the licence after contacting Embarcadero Sales and explaining the issue to them.
I managed to get through the installation process without any apparent trouble but I could not create or open any projects. Error "the required personality Delphi.Personality is unavailable" was always shown. The Platform Manager under Tools showed no available or downloadable platforms, and the GetIt manager was equally blank.
I tried everything that came up in a Google search, mainly from Stack Overflow and this forum: Uninstalling and reinstalling, restarting the PC a few times, starting Delphi 11 repeatedly with admin rights.
None of that helped.
So, in desperation, I copied the whole installation tree from the old PC (under "\Program Files (x86)\Embarcadero\Studio\22.0") as well as the public app data (under "\Users\Public\Documents\Embarcadero\Studio") to an external drive, and overwrote the installation on the new PC with it (because the installation paths are the same for the two PCs). I omitted "\ProgramData\Embarcadero" because there's only licensing info there and the two folders' contents was identical between the two PCs.
Next, I exported from the old PC the entire registry keys "HKCU\SOFTWARE\Embarcadero", "HKLM\SOFTWARE\Embarcadero", "HKLM\SOFTWARE\WOW6432Node\Embarcadero", plus a couple of CLSIDs, and then imported all of that into the new PC's registry. (All of the file- and registry key write operations on the new PC require admin privileges.)
This finally got Delphi 11 going properly without any warnings or errors and I am now able to create and open projects, and to compile them.
Cheers!