Hello festus77 and welcome to Apple Support Communities.
I see you are having an issue with not being able to delete the default smart playlists associated with the Music app.
These are not actually system-generated, per se. They are included with the Music app (and, indeed, versions of iTunes going back a number of years) as an example of smart playlists. If you call one up on the Mac, you should see an option called Edit Rules near the title of the playlist. As a test, I just deleted the 90s Music smart playlist from Music on a Mac, quit the app and reopened and the smart playlist did not return.
Try this. First delete the playlist from the iPhone by calling the playlist up and choosing the More icon (...) and choosing remove from Library. Next, shut down the iPhone, go to the Mac and delete the playlist there. Then reboot the Mac with the iPhone still off and open the Music app. If the playlist is not in the library, reboot the iPhone to ensure that it does not return when the connection between those devices is re-established.
Cheers.