Coolant in oil after overheating

The car overheated on the highway. It has no temperature gauge, but it gave an overheating text warning message on the screen to reduce speed and check the engine and it went into “Limp Mode. I slowed down and couldn’t stop safely for about a minute due to traffic. It seemed to have no coolant left in the radiator. There was a small puddle of coolant on top of the skid plate, possibly below the water pump, and some on the plastic radiator cover as well, near puddle location, on the passenger side of the car.

I let the engine cool down for 6 hours. I added the whole 7.9 gals of coolant which is the stated capacity of the system. But none of the coolant stayed in the reservoir at all. The radiator has no coolant filler cap. Still no coolant leaking out anywhere. Started then engine and still no coolant leaks. Stopped the engine.

Oil dipstick was covered in milky chocolate goo, so there is coolant in the oil. All that coolant I added seemed to just disappear, so could it I have gone into the oil pan somehow?

How do I diagnose this problem?

Could it be something fairly simple, like a blown intake gasket, or popped out freeze plug under the valve cover, or engine oil cooler failure?

Or is this always really serious like a blown head gasket or cracked block? And is the aluminum head always warped too much to machine flat and reuse after this happens from overheating?

Where do you think the coolant I added went, since it didn’t leak out?

What steps should I take to diagnose this problem?

Thank you for your help.