Lowering the supply temperature in underfloor heating more complex than expected?

With Styrofoam below and above the pipes, the energy primarily stays in the water and ends up in the return flow.
The main problem, as mentioned, is that the 30m of pipe under the tub obstructs the flow.
So no/almost no heat is given off, but at the same time the flow in the entire circuit is reduced, and thus the performance of this circuit.

At least you are now using no/almost no heat transfer in your wording. And maybe you somehow have a calculation after all?
My house has 20 cm mineral wool insulation on the exterior walls; the attic is even better insulated... I keep wondering why I have to heat?
I’m out of this discussion now.

Exactly, warm air is pulled out of the room with the highest desired temperature, the bathroom, and air from the cooler rooms flows in.

With 2 exhaust air vents in the bathroom and controlled residential ventilation, maintaining 24°C in the bathroom at 20°C in all other rooms becomes a real challenge???

With Styrofoam under and above the pipes, the energy primarily stays in the water and ends up in the return flow. The main problem, as mentioned, is that the 30m of pipe under the tub obstruct the flow. So hardly/no heat is emitted, but the flow in the entire circuit is reduced and thus the performance of this circuit.

That is very plausible. And yet the heat is not "gone", just not where it should be felt.

Exactly, you pull the warm air out of the room with the highest desired temperature, the bathroom, and air from the desired cooler rooms flows in.

You are of course absolutely right, but if it's only a 2 degree difference, and the heat sits in the thermal stores of the room and not so much in the air, that is not dramatic. The gap under the door is usually max. 1cm thick if done properly...

I recently had this discussion (reducing the supply temperature to 30°C) with our general contractor as well. He said he has to calculate based on 35°C because that’s what the standard requires. He must comply with this; otherwise, I could hold him liable in case the target values are not reached in practice.

[...]

For now, I accepted that since the contract entitles me to a turnkey house, and I can hardly demand every calculation in detail. Personally, I don’t like it, but unfortunately, that’s how it usually is when building with a general contractor. Before signing, I didn’t really think that this could become such a big issue.

That’s unfortunately how it is. Nobody thinks about it beforehand. But don’t let that stop you from still designing the underfloor heating based on a 30°C laying plan (if it is calculated (!) to be possible) and just not guaranteeing the temperature. Even with the 30-degree laying plan, you will be able to reach 35°C. But then you only discuss meters of pipe and laying distances, not temperatures.

In my case, I had thought about it beforehand, but my general contractor "had misunderstood." It ended up with me paying for the planning externally myself and paying a few hundred euros extra for wall heating in the bathroom. It was worth it to me.

Still on the thread topic: The most important insight for me so far in the discussion is that the investment (with GC: several thousand euros) is never worthwhile. For the few months you actually need to heat... And ideally, you have a photovoltaic system that reduces energy costs during the cooler months...

Because it’s actually just a few meters of roll, 2 larger heating circuit distributors, and 2 hours extra work for the GC. "Several thousand euros" is pain money to convince the crew to make an effort once and not just slap in the usual 08/15.

Unfortunately, that's how it is. Nobody thinks about it beforehand. But don't let that stop you from designing the underfloor heating for 30°C installation planning (if calculated (!) possible) and simply not guaranteeing the temperature. Even with the 30°C installation planning, you will be able to reach 35°C. But then you only discuss the meters of pipe and the installation distances, not the temperatures.

He did say in the further discussion that he plans the installation distances at 10cm and theoretically, we could run well below the 35°C flow temperature because of that. However, I can't see how that would fit with the planning. I will probably only see how the system is ultimately designed once it is installed; I will not receive planning in advance and I can't take that out as a separate trade either, unfortunately, he won't agree to that.

There is so much in house construction that you should read up on in more detail, but where do you draw the line when you have contracted a general contractor? In the end, the realization often comes: "I could have also contracted individual trades." But especially the ignorance about the processes in construction and the associated fear of doing something wrong, forgetting, missing something, etc., drive many into the arms of a general contractor. Once the construction really progresses and you start reading into the subject matter with the trades in parallel, doubts often arise – of course, too late.

But I still stand by my decision; I really have no choice left – think positive! :)

I will not receive a plan in advance

You have the right, for example, to check the heating design according to DIN together with an expert, which is being done in your house. Therefore, the general contractor must hand over the plans to you. Ask a (construction law) lawyer whether you are allowed to put him in CC when you write to your general contractor. Maybe gentle pressure will help. No one should legally be able to take away your right to control the construction execution. Please correct me or feel free to provide legal rulings.