The issue is solved. Probably an isolated issue on my side. I had to delete the app from the phone, install an older version of rekordbox (in my case 6.0.0.), install the rekordbox app on the phone again and connect it to rekordbox 6.0.0 and doing the first sync.
After that had been completed, rekordbox 6.5.0 connected again correctly with my phone and was able to interact with it.
The ticket I created earlier will be closed. Btw. Pioneer DJ contacted me on the ticket less than 2 hours after I created the ticket. Which was a very fast response.... lucky me. :-)