Hello grozix,
Thank you for participating in the Apple Support Communities! We understand that Apple Music is no longer working as expected on your Mac. We'd be happy to help point you towards a resolution.
Could you tell us more about what happens when you try to play music on the Mac? Does this occur with any song you try to play? With the Music app open on your Mac, let's also go to File > Library > Update Cloud Library in the menu bar. See if the playlists update to match what you see on your iPhone after that.
If there's no change, we'd like to have you create a new library, then see if you can replicate the behavior in a new library. Here's how to do so:
Use multiple libraries in Music on Mac - Apple Support
Cheers!