The brief
The Jetta had a faint fuel smell in the cabin after it had been parked, the morning crank had got noticeably longer, and there was a power dip when you asked for heavier acceleration. Three pointers at the fuel pump.
The fuel pump sits inside the tank and pushes petrol up to the engine at a set pressure. As it weakens, it can't build that pressure quickly on a cold start, which is the long crank, and it can't hold it steady under load, which is the power dip. And the pump module is sealed into the top of the tank by a large ring and gasket, so when that seal tires it lets a little fuel vapour escape, which is the smell. A pump giving you all three is on its way out.
The diagnosis
A pressure test confirmed the in-tank pump wasn't holding rated pressure under load, and there was a small seep at the module's top seal, which was where the cabin smell was coming from. The fuel filter checked out clean, so it wasn't a restriction.
That's a replacement. A weak fuel pump only gets weaker, and the next step is the no-start on the driveway, so it was getting changed now.
The work
System pressure was released, the rear seat lifted to reach the access hatch over the tank, and the failed pump module was unlocked and drawn out. A new VAG-spec pump assembly went in with a fresh seal ring, locked down properly so the top sealed clean.
Then the system was primed, the engine started, and the fuel pressure read on the gauge across idle and load to confirm it was holding spec, before the trim went back.
A road test confirmed it started cleanly, idled steady, and pulled away with the power back.
The outcome
No fuel smell in the cabin, a normal half-second crank in the morning, and no power dip under acceleration.
The Jetta went home running cleanly. A failing fuel pump gets steadily worse and then strands you with no warning, so acting on the long cranks and the smell meant a planned fix in the workshop rather than a tow.