What is the appropriate spacing for floor cooling installation?

It is not very ambitious. Our general contractor designs everything for 35 degrees. Financially, it is not worth it to go down to 30 degrees with four-figure additional costs.
I am specifically concerned about the cooling function, whether this could become problematic due to the 15 cm installation spacing.

For heating, a 10 or 11 cm installation spacing is better than 15 cm. A floor heating system is designed for heating, not cooling. However, a closer installation spacing is naturally also more advantageous for cooling.

Are you getting an air-to-water heat pump or a brine heat pump?

I can gladly show the planning. As I said, I am aware that the planning is not optimal.
The technical room and storage should actually also be heated. But our general contractor simply doesn’t do that in general.
At least we were able to convince him to install underfloor heating under the bathtub.

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As I said, my main concern now is the cooling, whether it can work like that.

We have an air-to-water heat pump.

Again... If the underfloor heating is properly sized for heating, then cooling is no problem. Your planning of the underfloor heating still has a lot of room for improvement. It can definitely be done better. This way you will only get a mediocre underfloor heating and cooling.

I would be interested to know if any of you use the underfloor heating with cooling function and have a laying distance of more than 10 cm.

As I said, my primary concern now is the cooling, whether that can work. We have an air-water heat pump.

An underfloor heating system is designed for heating, not for cooling. But a closer laying distance is of course also advantageous for cooling.

The "construction" shown in the plans seems to me like a foolish stunt / prank close to the Flat Earth Theory *LOL* I would never ever under no circumstances come up with the idea to use two media / two networks to regulate ONE single parameter!!! (in that regard, the idea of two laying distances seems p*rv*rs to me and as an overlay network only plannable by designated M.C. Escher experts, as well as a disturbingly exemplary testimony of a Pisa shock). Kelvin and his associates must be spinning in their graves when such things are thought of. is sorely missed here!

What do you think are the catastrophic effects of the planning? Apart from the higher supply temperature and thus poorer efficiency?

as I said, I am aware of that. It is miles away from Flow30. Nevertheless, the investment costs must also be included in the calculation. A 10% more efficient heating system does me no good if I have medium four-figure additional costs for the installation.