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Everything you describe sounds to me like it overheated, badly.
I think the initial problem was because it overheated, possibly because of a coolant leak. The mechanic probably correctly diagnosed the coolant leak, but didn't check the coolant level properly. He may have just checked the coolant level in the reservoir, and the radiator was still low. These cooling systems are hard to check correctly since the reservoir does not always purge over to the radiator correctly.
Continuing to drive the car with low coolant caused it to overheat even more and damaged the headgasket.
This engine is cheaper to replace than to fix the headgasket.
The transmission was possibly badly overheated also when the headgasket was damaged. This could have caused the valve body to sludge up or warp.
Or the wrong fluid/not enough fluid was put back in after the engine replacement.
I'm not trying to badmouth the mechanic, it just seems a little odd that it would overheat right after he gave you the all clear to drive it. Overheating on a Volkswagen is bad news.