After a long time of practice and waiting in vain for a FW update I downgraded to 4.3.3 today: Everything is fine again, my auto-leveling works again! Too bad I waited so long and lost so much wasted time.
I had the auto-leveling problems with the original Ultimaker print cores (both AA-0.4). Replacing the print cores and factory reset did not help. The XY calibration didn't work either, because the PLA of the Core-2 was not visible. Level-Switch Test worked without errors. I would say that also the inductive height sensor worked perfectly during calibration (by watch the spring screws), only the Z-value is not stored.
Note about the Ultimaker 3 firmware recovery work instructions:
Olimex board cover: This is the board with the Ethernet connector.
I couldn't find the status LED-Q LED-R and LED-T. But it doesn't matter, as the progress and completion of the recovery process is shown on the display.
In general: it was a easy and quick process.
During the welcome setup with the 4.3.3 I found something else: My NFC sensor is not connected because I use two separate spool holders. But I think this cause is rather unlikely.