Is it possible to effectively insulate the basement floor afterwards?

I wouldn't put myself through that. I've done something similar, but not because of the ceiling height, rather because of the insulation. Broke out the screed, put 10 cm of insulation on it, now floor heating is going on top. Just removing the screed was already a tough job. The base slab too... that will be much more difficult. Wouldn't the frost-free foundation have to be made deeper then?

If it's really only about insulation considering the room height, I would probably just use vacuum insulation panels, 2 cm would be enough. They are also more expensive, but much cheaper than breaking out the base slab. At most, just remove the screed and put in a dry screed. If the old screed was, say, 7 cm, you end up with 4 (2 cm insulation panel, 2 cm dry screed). At the ceiling... does there even have to be insulation if the basement floor is then heated?
With that method you would have better insulation and gain 3 cm - with reasonable money and effort.

Hello,

thank you very much for the tips and suggestions. The two rooms that we would insulate or increase the ceiling height of have a brick floor (approx. 7cm high). According to the architect, it could be removed without any concerns. We have already done that as well. The bricks could be removed without any problems. Underneath is initially just red sand. Presumably, below that is a leveling layer.

Feedback from the structural engineer in general is still pending. Furthermore, we would involve an energy consultant (who also provides construction supervision) to coordinate the further procedure. On the one hand, of course, you are right that the ceiling height in the basement for a guest room doesn't necessarily have to be increased. But another addendum, why we also considered increasing the ceiling height, would be as follows:

The house will also get a basement extension. The attached basement should (if you are already building new) have a normal ceiling height. The wish was now that the other two basement rooms (guest room and hallway (stair access from the ground floor to the basement)), which have a connection to the extension, become level with the extension. Hence also the desire to increase the ceiling height.

An alternative would of course be a step in the basement extension or to build the extension only 2.15m high. We have informally discussed our desired extension with a construction contractor. He said that he recommends "WU concrete" for the extension, and in that context, the ceiling height of the two old basement rooms could also be increased by lowering the floor and applying WU concrete there as well.
However, as mentioned, this has to be clarified with the structural engineer, architect, and energy consultant. To not be completely out of the loop as laypeople, I was therefore here in the forum to get some tips or suggestions. (For example, I find these vacuum panels interesting, especially if they are easy to work with.)

Best regards