This happens on one of my bikes with a steel frame.........the frame fills with water when left outside.

I assume it is the pedal crank group-set side cup that has rusted in.

Does the shell cup have flats on it? if so is it possible to get the flats into the jaws of an engineers bench vice and then turn the frame to unscrew the bearing cup; the whole frame horizontal is best. This method has never let me down when working on bikes up to about 40 years old and so far I have never needed heat.

When you have stripped the bottom bracket from the shell drill it to take a grease nipple. I prefer to use threaded conical grease nipples but a zerk nipple will do. Then you will want to cap the frame tubes internally. I use red plastic hydraulic pipe storage caps, and these pipe caps stop excess grease pushing up the frame tubes and water running down to the bottom bracket. Assemble the bottom bracket: I like to remove the balls from the carriers (and throw the carriers away) and install only the balls plus an additional one ball on each side and fill the bottom bracket shell with an EP2 general purpose lithium grease. Then once a month or so put a pump or two of fresh grease into the bottom bracket allowing a little grease to push out around the shaft.

My Falcon Explorer hybrid (like all my other bikes) had this mod done to it 11 years and 44,000 miles ago and I am still on the original bottom bracket and ball bearings and I only grease it twice a year if it is lucky!