Having underfloor heating milled in afterwards. Experiences!!!

I am also familiar with electric underfloor heating, but the question for me is: Can I actually heat an exclusively, let’s say, 6-7m² bathroom economically with it? In the past, as far as I remember, they were always advertised as an auxiliary heater -- for warm feet --.

It is a question of heating power whether it is about "floor heating" or room heating.
Of course, the heating surface (including that of the bathroom) should already have a size so that the heating power for the room is not only enabled at (here only meant humorously) 50°C surface temperature. But the system does work.
There are not many possibilities to consider, especially with the extent of remodeling measures, taking into account all the "pros and cons." Therefore, the question of economy does not arise here.
Example with purely hypothetically assumed numerical values:
you have to spend €10 more per month for electric heating, rather save that for economic reasons and therefore renovate for €8,000, but then have a norm-compliant structure - well, here this question actually arose, only with a different objective.
So: room heating with electric foil heating under tiles, that certainly works with the appropriate room size!

This is a very interesting topic (sorry for OT). We will also be renovating a bathroom in the next 3 years. It is 6.5m² in size (3.2x2.1m), but will be expanded by a walk-in shower, so a total of 8m². Since we have to reroute some connections (shower and bathtub), the screed will probably not remain intact. A underfloor heating could be relatively easily retrofitted, as the heating circuit distributor for the underfloor heating with a free connection is located directly in the hallway under the bathroom. There will definitely be a towel warmer later (currently there is also a radiator), so an electric underfloor heating might also be considered. The advantage would be the faster response, but I think the higher heat demand for the underfloor heating due to the additional room will hardly be noticeable financially and at the moment I have no idea what the electric underfloor heating consumes.

The financial effort for the underfloor heating installation can probably only be estimated once the tiles are removed. It would of course be great if you already had the numbers for the consumption values on the table beforehand.

Sanitary objects should be at least partially repositioned; the plan is apparently to solve this in the basement room below and more or less "only" drill through the floor. I need to have someone tell me at the next meeting what the sanitary company thinks about the whole thing.

Since I am currently involved in bathroom renovation myself (actually the whole house), here is my two cents. In our bathroom renovation (built in '59) it turned out that, unlike the rest of the house, there was no floating screed installed there at all, but it was poured directly onto the raw floor with waterproofing. Accordingly, everything had to be removed. After the connections were laid, there was not much left of the raw floor either. Even if in your case much is to be done from the basement, you will anyway have penetrations in the old screed at the old connections.

Given the usually manageable size of bathrooms, there are many reasons to simply replace the screed and completely build up the floor with proper insulation.

For "re-milling" as a simple/cheap and ecologically sensible alternative: mill NEW "screed".

For this, from the raw floor, lay full-surface cement-coated, fiber-reinforced XPS boards (construction boards, Wedi boards) up to the desired construction height/tile height, except where the shower and bathtub stand, and seal the joints. Now mill slots into the Wedi boards for the underfloor heating pipes at the required diameter and 3 mm deeper, lay the pipe/line, seal with tile adhesive, reinforce again, and done is the tileable, waterproofed, optimally heat-insulated, inexpensive bathroom floor with fast-reacting underfloor heating.

I discussed this in detail with my plumber and it is also recommended by Wedi. For old building renovations with low construction height, this is the best solution I have found so far. Of course, it also works with electric heating without milling in.

If everything is being replaced anyway: have you already thought about a wall/ceiling heating?