apple music no co-author button in playlist

• Are you an Apple Music subscriber?
• Do you have Sync Library turned on in Music Settings?
• Are you under 13?
• Have you set up a Profile in Apple Music?

Create an Apple Music profile on iPhone - Apple Support

You have to set up an Apple Music profile before you can collaborate with others. You don't need the profile to use Apple Music, but you do need it to share/collaborate music. That is done by following the steps in this link:

Create an Apple Music profile on iPhone - Apple Support

The only other thing I know of where you would not have the option to collaborate is if there are Screen Time Restrictions on your device preventing collaboration. If there are, turning off Content & Privacy Restrictions would then allow you to collaborate. If you are part of a Family Sharing plan, then it would be the Organizer that has control over the Screen Time restriction.

If that is not it, then I would recommend to contact Apple directly:

Contact Apple Support - Apple Support