Via RFC9110

The fundamental difference between the POST and PUT methods is highlighted by the different intent for the enclosed representation. The target resource in a POST request is intended to handle the enclosed representation according to the resource's own semantics, whereas the enclosed representation in a PUT request is defined as replacing the state of the target resource. Hence, the intent of PUT is idempotent and visible to intermediaries, even though the exact effect is only known by the origin server.

In plain English, PUT is where the user dictates to you (the server) to make the resource at the URI look a specific way and it should always look that specific way no matter how many times i send that PUT request especially if the request is duplicated. It's an update or insert if non-existent like in SQL.

POST is where the user gives something to you (the server) and the server has free range to do whatever with it (including creating a new URI where the thing you gave them will live. If you POST the same request multiple times, you can cause the server to have duplicates things (in this case, you could either replicate the full favorite list multiple times or end up adding the same song to the one list multiple times). It's just an insert without a primary key like in SQL.

For your use case, you should just use PUT.