Another interesting article by Jennifer Ashley Tepper, though I'd quibble with some of the examples. Eg I'd say The Sound of Music falls squarely into the "shows based on real show business people" category, and while Fun Home is based on a autobiography (by Alison Bechdel), Bechdel herself was not directly responsible for the musical's creation, unlike A Strange Loop (where Usher is very much a stand-in for Michael R Jackson) and Rent (drawn from Jonathan Larson's experiences). A Chorus Line is an interesting edge case.
I'll also add that Les Miserables is an example of a show based on historical events but not centred on real life figures. Many people may not know that the 1832 student rebellion depicted in the musical actually happened and that General Lamarque (of "Lamarque is dead" fame) also actually existed.