The brief
The Golf had been losing power under acceleration, the engine had picked up a vibration the owner could feel through the wheel, and there was a hesitation off the line. That's the classic misfire signature, and the usual first suspect is the spark plugs.
The plugs are what light the fuel in each cylinder, and they wear a little every time they fire. The gap opens up, the tip rounds off, and the spark gets weaker until a cylinder starts missing under load. That's the power loss, the shudder, and the stumble when you pull away. A set that's done a lot of miles will start doing exactly that, and the fix is a fresh set.
The diagnosis
All four plugs came out. They were well past the 60,000 km mark from the last change, so they were due regardless, and two of them showed fouling that pointed at tired plugs rather than a coil problem. To be sure, the coils were swap-tested between cylinders, and the misfire didn't follow them, so the coils were fine.
That made it a plug-only job. No point throwing coils at a car that just needs new plugs.
The work
Four new VAG-spec spark plugs went in, each one gapped to the manual's figure and torqued to spec so it seals and conducts heat properly. The coil packs were reseated on top with the harness clips clicked back home.
Then the engine was run at idle for a bit to confirm it was firing cleanly on all four with no stumble.
A road test confirmed the power was back and the hesitation was gone.
The outcome
Smooth idle, power back through the rev range, no hesitation off the line, and no misfires.
The Golf went home running cleanly. Plugs are a wear item, and once they're tired they drag the whole engine down with rough running and worse fuel use, so a fresh set was the cheap fix that sorted all of it.