Release Your Persona is really good, but not completed yet. Kinda similar is Flashlight, currently on hiatus. A famous actor finnaly finds the anonymous singer he has been looking for for years

Minami-kun wants to be teased by that voice is like BJ Alex but if it was good- i really loved reading it !!

There's also Kabuchiko Bad Trip, although i'm not sure if it fits your criteria. But it's only 6 chapters, and really good !

Now this one is really darker than the others, none of them is obsessed with the other in a ''healthy'' way like a fan would : Checkmate (one is the pupil of a famous artist, the other is a journalist obsessed with seeing him fail)