re: The Wrong Man--the only recording that exists is the concept album, though some of the cast members did quarantine performances on Youtube
I had Amazon Music as a trial for a bit, and they did seem to have more than Apple Music, though I didn't do an exhaustive search. (At the time Apple did not have Anastasia, the recent My Fair Lady, and The Lightning Thief, though it seems like they've added it since then, so it's possible they've increased their Broadway library recently.) It does seem that there's more people creating/curating playlists for Spotify, and generally their discovery tends to be better, but I like Apple Music because I can upload my own files to iTunes and have it sync (Amazon doesn't allow for file uploads) and Spotify's interface drives me crazy (along with the fact that I would've had to port over my pre-existing music collection anyway).
Apple's interface isn't the greatest either and I could go off an a whole separate tangent about that, but one thing to note is that their search is not exhaustive. For example, if I search "Follies" then the main albums show up but not the 1987 London one, though if I search it in iTunes, I can find it and it shows a banner saying that it's listenable in Apple Music, which has been my general workaround for things I can't find (this also tends to happen with newer albums). It'll also display these harder-to-find albums if you search a specific song ("Waiting for the Girls Upstairs" works in the Follies instance), so there's a couple avenues to try before knowing whether or not an album is actually on Apple Music. (Though on the other hand, based on the Hadestown tiered release, Spotify doesn't quite know how to do "pre-sales" or create a distinguished difference between playlists and albums, so pick your poison.)