For those unfamiliar with the term “diegetic music”, it refers to music that’s actually played in the story rather than just for the benefit of the audience. The characters can hear it too.
With that in mind, are there any musicals where the characters acknowledge that they’re constantly breaking into song? Buffy the Vampire Slayer’s “Once More with Feeling” is the best example I can think of for this.
In Once the main character writes a song that the plot of the musical revolves around. Hadestown too has elements of this. Neither are 100% diagetic but feature songs which serve the story.