You have to remember, the first Joker film was a big protracted and overlapping unhinged dream sequence, so I think escalating to a musical is quite in keeping with the premise. Last film it was a talk show (that may have never happened) and now it's a bloated stage performance that unfolds in his head. I get it, the guy is nuts and imagines glorified exhibitionist scenarios for himself.
I doubt the entire film is a long musical number, like The Sound of Music or Mama Mia... well, I hope it's not. Anyway, Lady Gaga is pretty talented as a songwriter and performance artist so I rather trust her contribution to the project. If she has a writing credit it might be because the song lyrics are relevant to and situated with the dialogue content of the screenplay. I felt like The Joker was DC/Warner's arthouse comic film and this sequel is no different, so if it stretches its experimental muscle beyond comic fan-fiction stuff then that's fine. That's what it was meant to do.