How to tell if motor is ok after over heating

1994 camry 3.0 V6, 221k, auto
My daughter called the other night to tell me her car had smoke coming from under the hood when she got to work. after work she drove to a friends home about 4 miles in city traffic and it did the same thing. I drove there the next day to look at it and it had no water in it. I added a gallon of water to the radiator and seen water start leaking out of the top of the radiator. the plastic radiator has what looks like stress crack as if someone may have leaned on the upper radiator hose.
I do not know how hot the car got and will replace the radiator if the engine is still good other wise i will junk it.

A compression test needs to be run; both a dry and wet test. A good engine will carry 180-190 PSI on a dry test but a high miles motor like this will have lower readings due to wear more than likely.
With lower readings a wet test should be done and if the readings jump up considerably that’s a sign that the piston rings are cooked/worn out.
Example. Cylinder shows 130 PSI dry and shoots to 170 wet means a ring problem.

You should also look for cylinder readings that are all within 10 PSI of each other.

To really assess the engine damage you could do compression tests, leak down tests, etc. to determine if the head and head gaskets are still intact. Perhaps a cheaper way is to fill up the radiator and run the motor for a period until the coolant needs another refill. Look for zero white smoke from the exhaust and overall power and smoothness of the motor.

If it seems OK, then replace the radiator and hope for the best.

Replace the radiator and crank her up with the radiator cap off. There probably will be some bubbles initially as the coolant starts circulating, but after the engine gets up to temp, look for a trail of tiny bubbles coming up through the coolant. If you don’t see any bubbles, that is a good sign.

Then you can do as OK4450 suggests, that is what a good shop would do before letting the car out of the shop, or you can just button it up and drive it, but watch for overheating. If the head gasket has been breached, you are unlikely to do any more harm. The damage, if there is any, is already done.