Hello dexxxtro,
Thanks for reaching out to the Apple Support Communities! I see from your post that the Remote app which is running on your iPhone X, running iOS 13.3, is not working with Music on your Mac, even after installing the latest macOS Catalina update.
You've done nice work testing out with another device and finding that you have to link the remote app manually for it to work. Based on that information, I would begin with these troubleshooting steps which will help to isolate the issue further:
1 - Quit Music on your Mac. If it will not quit, follow these steps to force it to quit: How to force an app to quit on your Mac.
2 - Restart your iMac: Go to the Apple menu in the top left corner of your screen > Restart.
3 - Restart your iPhone following these steps: Restart your iPhone.
4 - If the issue persists, restart in safe mode and test again: Use safe mode to isolate issues with your Mac.
5 - If still occurring in safe mode you’ll need to create a new user and test it out again. This article will show you how: How to test an issue in another user account on your Mac.
Let me know the results.
All the best.