The brief
The Jetta was vibrating heavily at idle, the cabin had grown louder with engine noise, and the engine was visibly rocking in the bay whenever the throttle came on. Three complaints, all pointing at the mounts that hold the engine and gearbox to the body.
The drivetrain doesn't bolt straight to the car, it sits on rubber mounts that let it move a controlled amount and keep its vibration out of the cabin. The main mount on this car is a hydraulic one, with fluid inside to damp it. When that mount tears and its fluid leaks out, and the transmission mount and the lower torque link wear alongside it, the engine moves around too much, so it rocks under throttle and every vibration comes straight through into the cabin.
The diagnosis
The inspection found it: the main engine mount was torn and sagging with its hydraulic fluid leaked out, the transmission mount showed matching deflection, and the lower torque link, the dogbone that stops the engine rocking fore and aft, had a worn bush.
With all three worn, the right call is a full set rather than one side. Putting one fresh mount against tired ones would just leave the drivetrain isolated unevenly and bring the car back for the rest soon enough.
The work
The engine and gearbox were supported, the failed main mount, the transmission mount and the lower torque link all came off, and new VAG-spec parts went on, torqued to spec in the correct order so the drivetrain sits where it should.
Then the engine was run at idle and under throttle to confirm the vibration was gone and the engine stayed settled in the bay.
A road test confirmed the cabin was quiet again.
The outcome
Smooth idle, the cabin quiet again, and no rocking under throttle.
The Jetta went home with the drivetrain properly isolated. Doing the full set, all three mounts together, means it's a job that's finished, and the worn mounts aren't going to come back one at a time, each one bringing the shake and the noise with it.