OK. I have really been annoyed about this and have gone through multiple new-installs with restore of my configs etc. - to just end up with the same issue over and over. I have tried different linux variants (virtualized on my QNAP NAS) to same effect.
In the end, I decided to delete my persistance data - so all data in the persistance/mapdb and persistance/rrd4j folders. Then a restart of OH3.2 and cleaning up all the initialization of items which are now all null - where my rules might expect them to have a value (I know, I should deal with this in the rules, but I am lazy).
Now, my installation has been running for >1 week without any issues and my persistance and charts works flawlessly.
This leads me to suspect, that as I have - over the last few years (!) have played around with my OH installation quite a lot, many references to now non-existing items and data existed in the persistance data files/db - which might be the cause for my problems. I saw that in my rrd4j persistance data (.rrd files) there were a lot of very old items listed (several hundreds), which I have not used for a long time and which are no longer part of my .items files.
I now consider the issue closed from my side - and just wanted to capture my experience and suspicion here, as someone else might benefit from this…