Hi,
If you meant for Apple Music, you’ll need to change your Apple ID for Media and purchases.
As you pointed out the fact you don’t want it changes everything else, changing Apple ID for media and purchases changes Apple ID associated to App Store and iTunes Store, and all settings associated with purchases (payment method, billing address, purchases made…etc)
However, it doesn’t affect the Apple ID associated to your iPhone, so it doesn’t affect data, backups, iCloud, photos, find my..etc
If you still want to change Apple ID associated with media and purchases, so be able to get Apple Music subscription associated with another Apple ID on your iPhone, go to settings/Apple ID/media and purchases/sign out
If you meant by saying “music” songs added manually through iTunes that are on the Music app on your iPad/iPhone, you can do what I wrote above too or just re-upload songs on iTunes using the other Apple ID.