Bathroom ventilation drips despite pipe insulation

Something like this:

Okay, I understand :-). I have no solution for this construction ...

IMHO, adding more insulation will not help. As long as you do not have a sufficiently large volume flow of exhaust air running permanently, the pipe will be cold on the inside despite insulation, because it is open at the top.

has a "condensate trap" - whether that makes sense or not is unclear.

It was correct to consider the condensate formation in the planning. However, the chosen solution does not work, my suspicion according to your sketch: The condensate trap is too high.

Layman's opinion:
You could have placed the exhaust on a (built-on) wall, then put a T-piece in the wall, condensate downwards, exhaust upwards. The condensate must not allow channel gases to enter your ventilation (AFAIK, it can be drained into the toilet cistern).

Better if someone who knows about this had planned it. Do you have any legal recourse? What was agreed? It somehow sounds like a makeshift solution with your consent ...???

No, they always do it like that ;-) The idea was certainly to place the exhaust at the highest point. A false wall or directly on the exterior wall (1.6 m kneewall) would have the problem of being much lower. I would be afraid that the wastewater vent would smell then, right? I think you just have to make it airtight... Right now there's a paper towel inside and it's super dry. Let's see what idea the construction manager has.

I would be afraid that the wastewater vent would then smell, right?

Yes, exactly, that's why you shouldn't combine the room's exhaust air with the ventilation of the wastewater pipe.

I think you just have to make it airtight...

Airtight and exhaust air somehow exclude each other.

You won't be able to permanently and safely prevent condensate from forming (or you won't want to: heated pipe). Therefore, the condensate has to be properly drained. There are solutions for that. But it must be professionally planned, not here in the forum and not just between the construction manager and carpenter.

(Out of interest: Is the bathroom interior?)

Has a roof window and is located with the narrow side against the exterior wall (1.6 m knee wall).