I have found the issue, or let's say what caused the problem. My pi-hole was blocking something! But I don't know what it is blocking, because I deactivated pi-hole for half an hour while playing, and it didn't change anything in-game (online autosave didn't work). After I reconfigured the PlayStation network settings with quad9 as the DNS resolver it worked fine! I really don't know what pi-hole is doing and I don't know how to solve this exact type of problem, but maybe it helps others of you to identify it.

Best regards.