Infinite loading of my Music library on MacBook.

Hi there, adam_netolicka.

After reading your post, it appears that the songs you've selected for your Apple Music Library keeps trying to download to your MacBook Pro on macOS Catalina. The only songs that do appear are those you've purchased or imported from CDs. We're glad to help with this.

Turn on Sync Library with Apple Music -- Make sure that "Sync Library" is on. You can find the setting in Music > Preferences. If it's on, turn it off for a few seconds, then turn it on again and see if your songs appear.

How to test an issue in another user account on your Mac -- Following the instructions in this article, create a new user account and see  happens there, then refer to the information below:

• If the issue doesn't happen in the new account, follow the steps under "If the issue doesn't happen in the other account". 
• If the issue is occurs in the new account, the steps to use are under "If the issue happens in the other account".

You’ll need to sign into the Music app with the Apple ID you’re using for Apple Music in this new user account, and turn on "Sync Library"

We'd also like you to try these steps:

1. Check to see that your Apple Music or iTunes Match subscription is active.
2. Check to see if you can load the iCloud library on a computer (Music for macOS, iTunes for Windows) or on music.apple.com with the same Apple ID.
3. Restart the iOS device: Restart your iPhone
4. Update to the latest version of iOS for the device: Update your iPhone, iPad, or iPod touch
5. Troubleshoot the network connection: 

• If the behavior is isolated to a specific network - you should work with the network administrator (who may be your ISP) to configure the network optimally for Apple products: Recommended settings for Wi-Fi routers and access points
• If the behavior occurs on all networks:
  • • Check for and disable (then remove) any VPN or mobile security software. 
• Reset network settings and test again. Please note, this will remove all previously connected Wi-Fi networks, APN and cellular settings, and some VPN configurations. If you're using iCloud Keychain, this data will also be removed from other signed-in devices.

Then, Navigate to Settings > Music > Sync Library and turn the toggle to off. Restart the device, then turn the toggle on. Allow the content time to load. This may take several minutes for larger libraries on slower network connections.

And finally, Sign out of Settings > iTunes & App Store and sign back in. Re-enable Settings > Music > Sync library. Allow the content time to load. This may take several minutes for larger libraries on slower network connections.

Be sure to perform the additional steps depending on whether or not the issue happens in the new user account, and get back to us when you're able with the results.

Let us know how that goes.

Take care.