Synchronising Imac music to iPhone does not work

I am working on iMac OS Catalina 10.15.7 and trying to synch my music from the iMac music app into my iPhone 13 IOS 18.4.

However in the iMac music app the system does not detect the iPhone. As you can see on the screenshot, the iMac bluetooth config detects <iphone Steven>, but on the left hand side in the Music app the device is not found, so synchronizing does not start.

Also on the iPhone side, the bluetooth configuration shows the iPhone <connected> to the imac (I even pasted this image via Airdrop from the one to the other):

Up till now I was able to permanently synch my music library without problems. I believe through one or another sys update this is now impossible. What am I doing wrong, or what can I do to correct the situation?

Thanks your ideas.