I was hoping someone would respond to this, as I’m also curious roughly what the split would be.
But from my limited knowledge, I feel like I can confidently guess that it would NOT still be 50/50. Probably not even close, unless the songwriter is even more of a high-profile name than the playwright.
Of course, I’m sure it also depends on how many songs, and how pivotal they are to the piece as a whole. If it’s borderline between musical vs. play with music, then maybe the split would be closer. But I’d guess that in most cases, the composer for a play with original songs would have a much smaller royalty than the playwright. Because presumably, the composer’s work isn’t prominently integrated enough for them to be considered one of the creators of the piece along with the playwright. Even in Peter and the Starcatcher there are only - what, maybe 3 songs? I can’t remember, but I don’t think it was nearly enough to earn equal billing with Rick Elice.
But like I said above, I don’t actually know. These are just guesses. If someone had more concrete insight, I’d love to read it!