I would advise taking taking the BB out and checking there to see how bad the rust is.
Also should take the seatpost out and shine a light down the seat tube and inspect.

I had a Miyata that had rust like yours that I thought was surface rust.
Come to find out after wrestling with the seat post for hours and finally removing it, the seat tube
down by the BB was almost all the way rusted through. Barely anything left, frame was toast