Hi there arthitsendev,
Thank you for posting to Apple Support Communities.
We understand you are unable to update you iCloud Music Library in Apple Music. Is that correct?
We notice you're running macOS Ventura 13.2 on your Mac. macOS Ventura 13.3 was released today. We recommend updating to this version as well as updating your iPhone to the latest version of iOS. This will ensure the software is up-to-date. After updating you can then test if the issue continues. Before updating software, it is always a great idea to ensure a backup. Here are some helpful links if you're not familiar with backing up/updating:
How to back up your Mac - Official Apple Support
Update macOS on Mac - Apple Support
Back up iPhone - Apple Support
Update your iPhone or iPad - Apple Support
Again, once you've updated, test to see see if the issue continues. If you're still having an issue, we recommend getting ahold of Apple Support next: Contact Apple Support
Take care.