Insulating cold workspace floor - but how?

Hello,

about 6 years ago I bought a prefabricated house from 1980.
We have insulated the outside with ~15cm, also about 50 cm into the ground, but the floor in my office is still constantly cold.
The floor consists of about 25 cm of screed & reinforced concrete beams.
Below is our unheated pellet bunker, which is why I can barely/not insulate the ceiling.
Therefore, the floor should be insulated with a covering that insulates as efficiently as possible.
The problem is that, due to the transitions into the hallway and other connections, a maximum height of 2 CM must be adhered to.
For both insulation and flooring.

Currently, the insulation consists of a plastic foil and a low-pile carpet costing €1.99 per sqm.
This is now completely worn out and should be replaced with something better.
And for that I would need your help.
What can be used?

At 2cm you might as well leave it, the effect will probably be zero. If anything, insulate in the basement. What kind of covering is in the study? Tiles? How about cork, it definitely feels warmer.

As written above:

Currently, the insulation consists of a plastic film and a short-pile carpet for €1.99 per sqm.

Unfortunately, that's all there is. Yes, I had already thought about cork. 5mm impact sound insulation underneath and then 12mm cork on top. But we have already installed cork in the bedroom and children's room. Unfortunately, it is not really abrasion-resistant. In the study, I slide around a lot with the office chairs and fear that the cork will not last long there.

A wool carpet would provide relief - but it costs significantly more than 1.5 ..

I don’t want to say that the price doesn’t matter, but I have no problem spending a few euros more if it’s done properly afterwards. The room is about 4 x 5.5m in size, so if the sqm costs 40€ or 50€, it doesn’t really make a big difference. I’d prefer to stay under 100€/sqm :) It can definitely be more than 1.99€/sqm. At the same time, I also want to properly fit the window into the wall, since the interior cladding is crap, the window protrudes about 1 cm into the room on the bottom left. Also, there’s a stupid granite window sill right above the radiator, which is why the room doesn’t get warm properly. So, drywall on 2 walls down, chipboards down, exterior walls insulated anew between the rafters, completely new electrical wiring, and also the floor. On such a nice construction site, as I said, it shouldn’t fail over 5€ per sqm, the main thing is that the room is completely finished for the next 10 years.

The fact that the windowsill extends over the radiator is usually intentional, because this causes the air to circulate nicely.

Is the radiator perhaps too small?

Can you maybe gain a few millimeters downwards? If you reach 45mm, you can install underfloor heating using the dry method.