How can I export my Apple Music Library file from iOS?

I have an Apple Music account which I use on my iOS devices (iPhone and iPad) ONLY.

On my Mac I have an 'old school' iTunes music library (mp3/wav etc files only) under a different Apple ID.

I now would like to be able to sign into and use my 'iOS only' Apple Music account on my Mac.

On my Mac, I can sign out of my 'old school' iTunes Apple ID and sign in to the 'iOS only' Apple Music account with no problem, but doing so does not bring the music library with it. I can see the 'Sync Library' option on my Mac, but the LAST thing I want to do is combine my libraries together.

Therefore I need to be able to obtain the music library file from my Apple Music account. How can I do that?