The brief
The Golf kept needing coolant topped up between services, the level dropping with no obvious puddle. He brought it in, which is exactly right, coolant that disappears is going somewhere and a slow leak turns into an overheat the day it lets go. When one of these loses coolant slowly, the water pump is a common source. The pump circulates coolant through the engine and the radiator so the heat goes somewhere, and on this engine the pump and the thermostat come as one module. As the pump ages the seal weeps a little coolant that the engine heat dries off so you barely see it, and the bearing starts to feel rough. A weeping pump doesn't reseal, and on these you change the module so the thermostat goes with it. So it needed replacing.
The diagnosis
A pressure test on the cooling system pinpointed it, the water pump module was weeping from its seal and bleeding pressure slowly, with the bearing slightly rough, which is the disappearing coolant. The radiator, the hoses, the expansion tank and the rest of the system held fine. That's a pump module replacement, with the integrated thermostat and a fresh seal, rather than chasing a weep that's only going to fail harder.
The work
The cooling system was drained, the old water pump and thermostat module removed, and a new genuine VW-spec module fitted with a fresh seal and the drive belt set back up properly. The system was refilled with the correct VW coolant, the air bled out the proper way so no pockets were left, and held under pressure to confirm the seals were dry. A road test confirmed the gauge sat steady through traffic and at speed with no overheating and no noise, and the level stayed put.
The outcome
No more coolant loss, the level holding between checks, the gauge steady, the engine warming up on time, and no noise from the bay. The Golf went home with the cooling system circulating properly again. A weeping water pump only fails harder, and the failure at the end is an overheat that can take the head gasket with it, so changing the module kept it to a tidy job.