I tried the power off / reboot cycle now more than 10 times.
I wonder why it still shows 6.A.039 in the fastboot screen, however the phone installed update 6.A.040.
Is it possible to re-apply the update manually? As far as I understand the above mentioned procedures in Device is corrupted after latest Android 13 update - #6 by yvmuell will wipe all data on the phone, which you might understand is not what I want to do on a phone that is in daily use.
It would be nice to also get an update on what @Pandalf did and whether it worked.