You can find out by having it checked again. Any vw dealer can run it and tell u that. However, typically when codes are cleared and car hasn't driven enough miles to reset, any attempt to check codes (like when inspecting prior to purchase) would provide a error code that basically says its not able to perform any diagnostic at all.
But with vw there are few "safe modes". Urs sounds transmission specific and usually it will only Operate in 2nd and 3rd gear. It could be the mechanic you got quote from doesnt understand how the pain in the bleep VW chips work and assumed the tranny is shot just due to driving it. But u can check by resetting safe mode yourself, and drive it and if u notice ANY Change in the problem its likely NOT a full tranny issue. Plus ive never heard of a car having no issues then the next morning a significant tranny problem requiring a full replacement.
To be honest it really sounds to me like there was a problem with the inspection prior to purchase. Either it wasn't done at all, or the person who did it skipped impt things/doesnt understand error codes/isnt a mechanic. It would be rare for even a novice mechanic to miss the issue (if its really that bad) because either the problem code would be present, a message that it cannot be tested period (cuz recently cleared), or driving it just a few miles would show the problem. My guess is clearing the codes properly will result in the tranny operating correctly and thus mean ita a smaller problem. But if not, you should have noticed the problem the night u bought it and the inspector screwed u. If the dealer pulls up that codes were cleared before u inspected it (should show the date or mileage at the time) u could maybe scare the seller into thinking u have enough to prove fraud and get something from him. Codes typically onky clear for 30 miles or less before reappearing so if cleared it would have been recently