Engine replacement

I have an 05 Passat TDI GL that was recently totaled. The engine had the balance shaft upgrade done to it. I still own the car as I have not settled with the insurance company yet. I have come across another 05 Passat TDI GLS with a bad transmission and am considering swapping my engine and transmission with the good car. What issues am I going to run into with the computer recognizing the engine and transmission or will it be as simple as unbolt and bolt back in and turn the key?

none go for it

Wait until you are fully settled (money in hand) with the insurance company before you do anything. And I really mean ANYTHING.

Go the extra step of considering a manual swap.

Just leave the ECU in the car it came in. Otherwise, plug and play