Yeah, that’s not good at all. Depending on how much braking was done, it may have been possible to salvage the situation if you hadn’t bled the brakes. But bleeding them guaranteed that the power steering fluid got to everything in the brake system rather than just sitting in the master cylinder.
The first thing that happens is that the seals in the master cylinder will swell and block the brake lines, which will prevent fluid from returning to the cylinder. That will lock the brakes.
Then the seals will disintegrate because they aren’t designed to stand up to PS fluid. That will fail the brakes entirely and you won’t be able to stop the car.
Because the PS fluid got all the way through the system, the same thing will happen to anything in the system that is rubber, which means your calipers and rubber lines are shot.
Best practice is to replace the brake calipers, master cylinder, and flex lines. Once you get the flex lines detached from the hard lines, flush brake cleaner through the hard lines to get all traces of power steering fluid out. If any is left in the system, then it will just contaminate the new stuff you install and you’ll end up in the same boat again.
An added problem with the hard lines is that the vehicle is old enough that if you live in a state that salts the roads in the winter, they might be sufficiently rusted that when you go to wrench the flex line off of them, you’ll snap the end of the hard line, which will require replacing that as well. The main difficulty there is in the routing - you can get a cheap line bending pliers at any auto parts store, and they’ll often have pre-flared line in the length that you need so you won’t have to worry about flaring it yourself.
(btw @Bisbonian) I suspect the “overheating” was actually the power steering fluid overheating in the brake system and spilling out of the master cylinder and dripping down onto something hot. PS fluid is not designed to handle the temperatures that brake fluid sees, so it tends to expand enough to overflow the reservoir under enough braking.