Comes from the Eminem song Stan, about an obsessed fan named Stan.

It's also a portmanteau of "Stalker" and "Fan" allegedly, although my first awareness of it was the Eminem song you mentioned.

from the eminem song stan (also possibly from super-fan)

'T' is the second letter of the name 'Stan', the obsessed superfan in the song.

I had heard the folk etymology "stalker fan"

It's a reference to the name Stanley, 'stan' is the signature at the end of letters being read in the song

Stanley is a toponymic surname, a contraction of stan (a form of "stone") and leigh (meadow), later also being used as a masculine given name.