[DJCarbine]

I think by timing belt you mean the accessory belt, sound like it failed and the alternator/Bat light came on, then with nothing to drive the waterpump the car overheated. PS still worked because its electronic, but likely failed when there was insufficient power to drive it as the battery was running everything at that point.

Best case would have been to pull over once the alt/bat light came on

Best case scenario now is it didn't overheat to the point of warping heads and you will be fine with a new accessory belt and refilling of the coolant. Can you tell where the coolant came from? Did it vent from the cap/overflow?