Is further additional insulation absolutely necessary?

You can see it from the numbers. The insulating effect of stone is hardly present. That’s why good winter jackets also have down or synthetic materials that insulate well (they contain a lot of air). I don’t see a heat pump working for you without external wall insulation unfortunately. Then rather gas or possibly pellets.

but if I see that correctly, then I only need to install 150 mm EPS and then everything would be absolutely sufficiently insulated, right? Would a heat pump make more sense then, with existing underfloor heating? Regardless of a heat pump, façade insulation would probably be sensible here anyway, right? Or should one first insulate the roof again and the basement ceiling?

I have a detached house built in solid construction with the following masonry: - 11.5 cm KSV 1.8/250 + 2.0 cm Styrofoam + 17.5 cm KSL 1.4/150

In which year of construction was that part of the current humor trend?

but if I see it correctly, then I only need to apply 150 mm EPS

Yep, then everything looks completely different.

Would a heat pump make more sense then, with the existing underfloor heating?

That depends on the design (spacing) of the underfloor heating.

Regardless of the heat pump, a facade insulation would probably make sense here anyway, right? Or should one first insulate the roof again and the basement ceiling?

Insulating the property is not wrong, but just insulating would be the wrong approach. I recommend you consult an energy advisor so that you might also get funding. Because it doesn’t help if the facade is insulated and the heat then escapes through the roof, windows, front door, basement. Or if the spacing of the underfloor heating pipes is so large that hot instead of warm water has to flow through to make it warm.