Yes, I did check the CEC-adpater settings in the past because I was rather sure that the issue would be solved around there, but I did not find anything useful.
In fact, the solution actually is there - but sadly it's disguised behind some bad German translation. Picture for reference: deactivating the very first entry does the trick! Roughly translated back to English this entry reads "Upon starting announce Kodi as active source". There is no word about starting or powering on the TV or whatsoever - at least not for me.
My case 2 now works as desired. Case 1 got a bit more inconvenient than I expected because now I need to scroll down a quite long list of (unconnected) sources/devices on my TV before I can use Kodi - this is btw what I thought would be done by the first option in the settings. But overall this is still an improvement. Maybe I can work around that "scrolling through sources" inconvenience, too