Very thin screed, earth underneath - what to do?

As far as I can see now, there are the following two options: 01. Consider the rammed concrete as a raw ceiling and apply a moisture barrier, 6cm insulation, and 6cm screed on top. 02. Tear out the rammed concrete, dig deeper, possibly also add fill material, and then apply a moisture barrier, 6cm insulation, and 6cm screed to maintain the room height.

As far as I can see, there are the following two options:
01. Consider the rammed concrete as a raw ceiling and apply a moisture barrier, 6cm insulation, and 6cm screed on top.
02. Tear out the rammed concrete, dig deeper, possibly also add backfill, and then apply a moisture barrier, 6cm insulation, and 6cm screed to maintain the room height.

Option No. 1 is of course the easiest variant. And with good PUR/PIR insulation, you can get quite far. Although more would of course be nicer (thinner screed would also be possible, even with underfloor heating).

In variant two, it would be even easier to install underfloor heating.

What would be the minimum construction in variant 1? In my answer, I only quoted approximate values. Is impact sound insulation necessary even if there is only a ground floor without a basement and without a first floor? In other words: is impact sound also transmitted to adjacent rooms?

How should the new screed be constructed on the rammed concrete? Floating?

I unfortunately can't tell you either – when it comes to floors, knows best – but I estimate floating here to be pointless, it's hard to glide on such rough seas ;-)

Electric underfloor heating is also pointless without insulation.

Using wood chips from your own forest first to generate electricity for the heating would also be nonsense times three *LOL*

I would definitely clear everything out and dig. If you just build up, the door heights won’t fit anymore. New lintels are also quite a hassle. With a mini excavator, it should be doable, just a few centimeters are enough.

How do I prevent walls from sagging or cracking in variant 2 when I come too close to them while digging?