I found some time to diagnose this issue:
I typed *#*#2886#*#* in the phone app, got an encouraging green PASS.
Then I used MANU and selected “FINGERPRINT RAWDATA” and I got the result:
Electric test is OK
Sensorpix test is OK
I found this thread about a previous update https://forum.fairphone.com/t/fp5-fingerprint-sensor-unresponsive-after-update-098-not-0-88/115560 . There someone suggested a workaround “Disabled and enabled back Find My Device toggle. Now fingerprint unlock works.”.
Unfortunately “Find My Device” is active, but I can not deactivate it! Not sure if I ever changed it.