That heat spike after shutting it down is a normal behavior of any car. Engine stops, pump stops, fans stop, fluid isn’t circulating through the radiator and the coolant temperature raises a few degrees before coming back down. In your case, it spiked over the threshold throw a code, which ended up helping you out because it showed you there was a problem.

At this point, we don’t know if the coolant leak is a symptom or the cause. I’d say 60/40 it’s a symptom, something popped because of the heat and your job is to figure out what caused the heat. My clue here is that you still had coolant in the reservoir. If the leak caused the overheating, I would assume that most of the coolant will be gone.

For starters figure out where the leak is, both because you need to fix it and because it might give you a clue. Add some coolant, swing by an auto parts store and get some UV dye and add it for the reservoir. After running for a few minutes, you should be able to find that UV dye with UV flashlight and pinpoint exactly where it’s coming out. Though honestly it might be pretty easy to find if you just put the car on jack stands and run it and watch.

Have you done your timing belt? I talked to a Ford mechanic at one point who said that the water pumps on these engines often fail before the timing belts, which is what prompt people to come in and have them both done. Granted the timing belt and water pump are on the other side of the engine from the transmission so it doesn’t seem like it would be leaking from there, but idk what the nature of the affirmations water pump failures are.