Hi estrobink,
Thank you for participating in the Apple Support Communities. We understand you'd like to stop receiving notifications when an artist you've favorited releases an album. This article explains how to turn these notifications off: Add and see your favorite artists in Apple Music on iPhone, iPad, Mac, or Android - Apple Support.
"How to turn notifications on or off for favorite artists
You can get notifications for favorite artists only on iPhone, iPad, and Android. Notifications for favorite artists isn't available on Mac.
Turn notifications on or off for favorite artists on iPhone or iPad
- Go to Settings > Notifications.
- Tap Music.
- Turn Allow Notifications on or off.
- Scroll down and tap Music Notification Settings.
- Turn New Music on or off.
Turn notifications on or off for favorite artists on Android
- Open the Apple Music app.
- Tap Listen Now.
- At the top of Listen Now, tap the More button , then tap Account.
- Tap Manage Notifications.
- Turn Artists and Shows on or off."
We hope this helps.
Take care.