In The Office (US version) it is revealed that the mockumentary the viewer watches does in fact exist inside the universe. Dunder-Mifflin crew is even interviewed as stars of the show and Pam has a thing for the boom mic operator who worked on the set.
Netflix’ Tick tick boom is based on an eponymous theatre play, which told the background story of the shows creative process. Its main character is a fictional version of the creator, Jonathan Larson.
Season 4 of the Arrested Development revolves around Michael getting release rights from his family members to create a show based on their story from seasons 1-3. He even hires a fictitious version of Ron Howard, who is the real show’s director.
Marvel’s She-Hulk ends with the main character discussing the corners cut during production with a fictionalised version of Kevin Feige.
These are for examples that I could come up with from the top of my head. Can you think of any other?
Not exactly what you asked for, but Dr. Horrible’s Sing-Along Blog had a director’s commentary track that was also a musical.