What enlightening info can I still give? If I even know it at all, I admit that I have zero knowledge of the subject and have to painstakingly read up on everything. But it's like in medicine....the big picture still doesn't become clear from that.
From my point of view, everything is okay.
You don't have to justify yourself here.
You were quoted an extra price for the underfloor heating.
That seems high. Yes. True. And you have the "?" in your eyes. Understandable.
Considering the house price - your house is certainly not in the low-budget league - that's still okay.
As I said, even in my little place, which would probably fit as a model-show house for a Christmas decoration by comparison to your house with all the space on the ground floor, they wanted 8K more for it.
You simply ask your general contractor now about the reasons for the additional cost and have it broken down for you. Maybe there is still something to save, as someone said here, there are regulations around 30/piece or 300. With 10 pieces, we'd already be at 2.7K. They have to answer to you on this - you then make the differential diagnosis yourself in the end.
If you don't have an aversion to underfloor heating (like me), then build your large and certainly representative house with the underfloor heating. It clearly increases its value, as most people also inquire about such things.
Best regards
Thorsten