Almost certainly intentional
A sound recording - which is what you are listening to in Apple Music - is protected by Copyright -
https://en.wikipedia.org/wiki/Copyright
Those "rights" typically include reproduction, control over derivative works, distribution, public performance, and moral rights such as attribution
A screen recording while Apple Music is playing is reproduction of the original sound recording.
In making your screen recording, you are creating your own copyrighted work that would be a derivative work of the original sound recording
The song itself - lyrics and "sheet music" - are a different copyright held by the composer(s)
see the sections
in the Wikipedia article linked above