Garage height - which floor structure (height issue)?

We have a small height problem with our garage. The garage is only planned to be 2.25 m high. If 6 cm of screed are added on top as in the plan, only 2.19 m remain. I am currently planning the driveway so that at least a 2.125 m door can be installed. However, the screed is always in the way because of the installation height. What do you recommend in such a case? I was thinking either to grind and paint the floor slab (sealing, etc.) or to tile without screed (with a mat underneath?). Is something like this feasible?

Is there a passage into the residential building? - in a garage, you don’t have underfloor heating, so 6 cm screed thickness seems quite generous to me. In the basement of a rental building, I never missed a simply omitted screed. For a garage floor, I would apply a coating that makes sweeping the floor much easier compared to the completely raw concrete. What is the construction height of the threshold of the gate?

Yes, there is a door to the basement of the residential building. It will also be the main entrance for residents who come by car. What exactly do you mean by the construction height of the threshold? The lintel? It should be 11.5 cm high.

Grind the concrete and leave it as is, without painting. --> Looks great (a friend of mine did it like that)

What exactly do you mean by the construction height of the threshold? The lintel? That is supposed to be 11.5 cm high.

The threshold is the lower counterpart to the lintel. With sectional doors, it can be very flat; with up-and-over doors, the strike plate also has to be attached at the bottom. In the mentioned basement it was like this: the staircase had a marble floor, the basement floor was raw concrete, and apparently 4 cm or a bit more of screed height was planned. But there was none, so only a mortar wedge was rammed up to the end of the marble floor. From a user's perspective (for a storage and workshop basement) this was no quality difference; the missing screed was primarily noticeable in the height of the lower door gaps.

Grind down the concrete and leave it as is, without painting. --> Looks great

In one garage, I had bare screed, and in another one with paint on top; that made a significant difference when sweeping. You can hardly grind it so smooth that no dirt settles into the "pores." With paint, you can even mop. Currently, my steel garages have interlocking pavers or sidewalk slabs; cars find that nice enough.

Consider that salt and concrete are enemies, a simple coating is not the right solution there.

It must be sealed.