I don’t recall what I was listening to when this popped into my head, but I was curious about the origin of fan used to mean a “supporter” or “devotee.” I recently installed Terminology across my devices and set the Online Etymology Dictionary as a preferred resource.
According to them:
1889, American English, originally of baseball enthusiasts, probably a shortening of fanatic, but it may be influenced by the fancy, a collective term for followers of a certain hobby or sport (especially boxing)… Fan mail attested from 1920, in a Hollywood context; Fan club attested by 1930.
I’m pleased that the best-guess origin is with baseball.