Remote Music Purchases Not Appearing Properly in Music Library

When I buy a song using my iPad [iPad OS 16.3] that song is added to my main Music Library root folder only - not where it should reside - neither in a folder marked with the artist's name nor in a sub folder under the album name as they should be and indeed are when I purchase songs using my MBP 2019 [macOS 12.6.3].

Songs so purchased do show up in the "recently added" category in the Music Library dashboard and can be played via the dashboard, but Music Library can't seem to find them.

In order to fix that, I have to manually navigate to the iTunes Media/Music folder, create a new folder for each new artist plus an album sub-folder for that new artist or an existing one, then navigate to the iTunes Media/Music root folder to drag and drop the individual song or songs to each appropriate artist's album folder. Manually. That's for songs purchased on my iPad.

Songs purchased using my MBP running my default Music Library directly do not have this issue. They show up in the iTunes Media/Music folder stored in the appropriate artist folders and sub-folders.

How do I fix this short of never buying songs using a remote device again?