I have the Meowlody trophy but no music badge?

[FrightZone82]

Just finished the game and now doing a second run to clear up things I missed.

I only have three badges on me, Cat, Outsider and Police. 
And yet I did get all the music sheets back in the slums as I have the trophy for it.

So not sure why i don’t have the music badge?

I went back to chapter 6 and now Morusque doesn’t have any sheets frustratingly, I was hoping not to have to do it again.

Any ideas what went wrong?