Or, at one point, the Qax in Stephen Baxter's novels, although they evolve as patterns of turbulence in fluids, and then somehow transfer themselves to the solar atmosphere. Communication difficulties there were mostly caused by the Qax being arseholes.

There must be a list of fictional alien races living in stars, but i couldn't find one with some quick googling.

Not sure if there is a list, David Brin's Sundiver [0] is one example of a novel with a fictional alien living in a star.

[0] https://en.wikipedia.org/wiki/Sundiver