I can also make the shotcuts work by using the global hotkey to open the Enpass Assistant, select an entry and open it by either clicking the "i" or using the right-arrow key, so that I see the entry's attributes (username, password etc..). After that Ctrl + Shift + P start working (also from the list of entries, no need to open the entry itself). I also checked the whole behavior with my private computer which - besides running windows - has nothing in common with the PC I use at work.
By the way: No answer in over 10 days in this forum which seems to be the wanted way to ask for support, since the Support Page of the Enpass homepage only links to the User Guide or to this forum.
I also wrote a mail on April, 8th and got a very fast response from the Enpass Support Staff (Pratyush Sharma) that QA will look into it. On April, 11th I got a mail (apparently from a mailbot) that the case is closed because I did not write back. I'm not satisfied.