@pocket: Thanks for your hints in troubleshooting. All of them make definitely sense. Some of them I already did as you said. I will take them into further consideration.
@DrewXT, right this is what I already excluded several months ago and therefore I moved my HA installation from SD card to SSD - see SD card failure on Pi4 - #6 by Red1.
With this move I hoped getting rid of the HA crashes as I experience today from time to time. But seems that I was wrong.
Offloading the database might be a way. But for the moment, I guess that the SSD should be able to handle it.