Hi there Dessi34,
I understand that in the Alexa app you're seeing a message that Apple Music is linked but it is not functional. Listening to Apple Music is something I personally use daily, I'd be glad to assist in seeking a solution.
Below is a resource that can help:
Listen to Apple Music on the web and in apps
This resource provides great information on the ways apps and websites can access your Apple Music subscription and ways you can control access.
If you still need further assistance after checking out the resource above, you can always reach out to the app developer as well with this resource below:
How to contact an app developer
Have a great day!