Thanks a lot for your quick and finally helpful response, Ilian Gachevsky!
Install with apt did not work for me, I only got 13.0. Indeed I succeeded to download the install-wolfram-engine-13.3.1.sh file on my Windows 10 PC. But it did not install correctly on my Raspberry Pi. Now I suspected that the problem could be my old 32 bit Bullseye Raspberry OS. Indeed installing and running 13.3 worked like a charm on the new 64 bit Bookworm OS!
Does 13.3 work only on 64 bits and/or Bookworm?
