Mill underfloor heating or apply new screed?

That is then a reasonable insulation - it definitely does not replace insulation of the basement ceiling. Less insulation (both thickness and quality) is hardly possible. Either directly with a PUR insulation (although I would still find the thickness too low) or simply 8cm PUR under the basement ceiling.

Thank you for the quick and helpful answer! Was that irony or is the insulation of the screed really reasonable? Does the PUR insulation refer to the basement ceiling? Can you manage that with a little skill yourself and what (material) costs should one roughly expect? I quickly googled it and found various offers (partly for flooring), sometimes PUR, sometimes PIR. According to initial research results, PUR apparently has a more balanced material distribution than PIR.

Is there a heating load calculation to ensure the house heats reasonably (heating costs) with these data? With 140 sqm and 12.5 cm, about 950 m of tubing will be laid (normal underfloor heating usually has 16/2 or thicker pipes). Then the 11 circuits are sufficient. Classic underfloor heating with 10 cm spacing (more effective, as lower supply temperature is possible ==> more suitable for future heat pumps) and 16/2 pipes of course provides a significantly better heating performance. I WOULD remove the screed and find a plumber who allows own work (tacking underfloor heating pipes). You will definitely find one via portals or eBay. Heating design calculation should be outsourced (e.g. Heckmann).

We do not have a heating load calculation. Is that recommended? And if yes, do you need an on-site appointment and what costs would one have to expect? Maybe these are also eligible for funding under the BAFA heating renewal program?! Is it even possible to use larger pipes with a milled underfloor heating? What exactly do you mean by "950 m of tubing" and 16/2 pipes? We have also considered tacking the underfloor heating ourselves and have already been offered that in principle. I have looked into it; there really are many systems for (new) installed underfloor heating. Recently I also saw the systems from Schlüter (with decoupling mats) (designation: "Schlüter®-BEKOTEC-THERM"). Have you ever heard of it? It apparently makes sense especially with a low build-up height. But hopefully we have no big problem here.

Thank you for the quick and helpful answer! Was that irony or is the insulation of the screed really reasonable?

Sorry, there was a missing "k". It is a simple standard insulation, which is better than nothing but doesn’t seriously prevent the heat from the basement.

Does the PUR insulation refer to the basement ceiling? Can you manage it yourself with some skill and what (material) costs should you roughly expect? I quickly googled and found various offers (partly for floors), sometimes PUR, sometimes PIR. According to initial research results, PUR apparently has a more balanced material distribution than PIR.

PUR/PIR referred to both sides of the ceiling. You can put it under the screed and/or under the basement ceiling. The work is also standard – glue foam and stick it to the ceiling (possibly support it with cheap props). You just have to tinker a bit if there are pipes on the basement ceiling. And since you indicated NW as a federal state and your nickname somehow looks like Ruhr area, I recommend a trip to Nettetal for the insulation materials. There you can get second choice – more than sufficient for the basement or similar (I often go there).

We don’t have a heat load calculation. Is it recommended? And if so, is an on-site appointment necessary and what costs must be expected? Perhaps these are also eligible for funding under the BAFA heating renewal program?!

Recommended, yes, because with that you can properly size your heating + underfloor heating (including hydraulic balancing). On site? No, all online or by email. Costs are manageable – AFAIK also eligible for funding. For example like this – then you also get the installation plan for the underfloor heating.

Is it even possible to use larger pipes with a milled underfloor heating? What exactly do you mean by "950m tubing" and 16/2 pipes?

I believe the milled UFHs only use pipes that small. About 950m of those will be installed in your case. Larger pipes, like for a “normal” underfloor heating, start at a diameter of 16mm (wall thickness 2mm). Significantly more water can flow through those – so a lower flow temperature can be operated. With a spacing of 12.5cm, it’s about 950m of the 14x2 pipe. If you switch to 10cm spacing, it’s already 1,230m of pipe. More or less like having larger radiators. They give off the same amount of heat at a low heating water temperature as smaller radiators do at a higher temperature. And then you also have more heating water flowing through larger pipes. But also more heating circuits. I even installed mine myself often at 7.5cm spacing – on 120sqm that was over 1.5 km. The "extra" material effort is, in my opinion, no obstacle, as it's not that much more expensive.

We’ve also considered stapling the underfloor heating and were offered that in principle. I looked it up; there are indeed many systems for (new) installation of underfloor heating. I have most recently also seen the Schlüter systems (with decoupling mats) (designation: "Schlüter®-BEKOTEC-THERM"). Have you heard of that? Seems to be suitable especially for low buildup heights. But hopefully, we don’t have a big problem here.

Heard of it, never used it. Last time I just laid insulation on the floor and glued a grid foil on top. Then simply stapled the pipes onto the insulation/foil. Laborious but quick and doable without much prior knowledge.

If you install and staple it yourself, by the way, you have absolutely no warranty claims against anyone in case of damage.
It will always be spun in a way that you caused the hairline crack in the pipe yourself because you stapled incorrectly or stomped on it like an elephant ;)

Whether that is ultimately worth a few thousand EUR in savings... depends on whether your floor is wet at some point or not...

PS:
Almost everything in construction is doable without prior knowledge. But you are also to blame if it goes wrong because you had no idea how to do it properly or didn't know the critical points that matter.

By the way, if you lay and staple yourself, you have absolutely no warranty claims against anyone in the event of damage.
They will always twist it so that you caused the hairline crack in the pipe yourself because you stapled incorrectly or stomped on it like an elephant ;)

Whether that is worth a few thousand euros in savings in the end... depends on whether your floor is wet at some point or not...

PS:
Almost everything on a construction site is doable without prior knowledge. Only you are also to blame if it goes wrong because you had no idea how to do it properly or didn't know the critical points that matter.

Thanks, I wanted to contribute that as well. Since I’m currently facing the same issue myself (stapling underfloor heating pipes). In the end, I had the heating engineer do it, precisely because of the warranty background. It would have been about €1200 in savings if I had done it myself. But any claims in case of defects and the consequential costs would have been lost.

Almost everything in construction can be done without prior knowledge. Only, you are of course also to blame if it goes wrong because you had no idea how to do it properly or didn’t know the critical points that matter.

That’s exactly why you do it together with the heating engineer. Lay and staple yourself. The heating engineer handles the connection (presses the fittings) and assumes the warranty. A very common procedure in construction. That’s also how I recommend it.
When I do things myself, I do everything completely on my own – at least then I know who screwed up ;)

Exactly why you do it together with the heating engineer. Lay and staple yourself. The heating engineer takes over (presses off) and assumes the warranty. Completely usual procedure on construction sites. That's how I suggest it as well.
With me, I do everything myself - at least then I know who messed up ;)

I suggested that too. Mine refused. Either he lays and presses off, or no warranty. Seems there are regional differences on this topic.