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

Have you calculated that, tried it out, or is it just a feeling?

Are you so convinced of your version? I haven't calculated it, but my common sense tells me that. I am happy to read through your calculation now.

He said he had to calculate based on 35°C because that is what the standard requires.

This is also one of those statements where the general contractor takes the easy way out so that you as a customer do not question further. Because a) there is no such standard and b) the 35 degrees come from a DIN and refer to a maximum surface temperature for underfloor heating (applies for edge areas, 29 degrees for main areas). It’s just annoying how you get fobbed off...

but my common sense tells me that

Physics surely has an answer. I guess the law of conservation of energy? The heat energy from the pipes under the Styrofoam holder of the bathtub goes somewhere too. Whether into the concrete ceiling / screed or elsewhere – the energy stays inside the house. Whether you can feel it in the bathroom is another question. Or am I mistaken? And one more thing to consider: with controlled residential ventilation, the heat is also distributed again throughout the house...

Still on the thread topic: The most important insight for me so far in the discussion is that the investment (for the [GU]: many thousands of euros) is never worth it. For the few months when you have to heat... And ideally, you have a photovoltaic system that reduces energy costs during the cooler months...

Physics certainly has an answer. I guess the law of conservation of energy? The heat energy of the pipes under the styrofoam holder of the bathtub also goes somewhere. Whether now into the concrete ceiling / the screed or somewhere else - the energy stays in the house.

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 they give off no/almost no heat, but reduce the flow in the entire circuit and thus the performance of this circuit.

And one more thing could be considered: With controlled residential ventilation, the heat is distributed again in the house...

The effect is extremely small

And ideally you have a photovoltaic system that reduces energy costs during the cold months...

Yeah, you should have a photovoltaic system, but especially when the heat pump really has to work hard, usually nothing comes from the roof.

And one more thing to consider: With controlled residential ventilation, the heat is also distributed again throughout the house...

Exactly, the warm air is drawn out of the room with the highest desired temperature, the bathroom, and air from the rooms that are desired to be cooler flows in.