Catalina's Music.app never matches songs, instead it gives you a DRM-protected song
Apple Music is supposed to cover all iTunes Match functionalities. This is clearly stated on the official iTunes Match service page.
It always has been that way: when you added an external song, e.g. ripped from a CD, to iTunes, it matched it to the 50-milion-song iTunes Store library. It appeared as "iCloud status: Matched" and "Type: Matched AAC audio file", or "iCloud status: Uploaded" if the song was not found in iTunes Store library.
In Catalina's Music.app it correctly matches the song, but then it appears as "Type: Apple Music AAC audio file" and if you try to delete it you are warned that "The copy you are deleting is not stored on other computers...", and when you re-download it it is just an unusable .M4P DRM-protected file.
MacBook Pro with Touch Bar