Measure those cantilever studs. There are two standards, and the modern one is farther apart. It might be 60 vs 80 mm or something like that -- check it against a newer frame if you can.

If, as I suspect, this frame has the old standard for canti studs, it's tougher to find a brake that will work well. And vintage cantis, like old MAFACs can cost a fortune.

So, here's one possible way forward:

Throw out the fork.

Get a new 1" fork at a bike swap for $20 to $40 that either has a drilled bridge for a brake or modern canti stud spacing.

Run it with a front brake, fixed rear. Don't spend more than $200 or so making it a ride able six-pack hauler with a rack on the back.

Or just ditch it. It's not the kind of frame you want to be agonizing over.