You car probably has engine code AHU. There are a few of an earlier engine in the car, code 1Z, but they're uncommon. And the differences between the engines in the Jetta aren't that significant unless you're rebuilding it. There should be a sticker in the trunk by the spare tire that shows the engine code, but I suspect they're not always accurate.
Regarding the low power, MAFs aren't a very common failure item in A3s. Replace the vacuum lines first, including the hose in the ECU. and you may need an N75 valve. I'd look at those first as sources of low power. Plugged catalytic converters causing low power are common, too, in high mileage cars.
The TDI isn't a VR, but it'll pull well from low revs when running properly.