Air heat pump or use gas and solar?

Is the basement insulated from the ground floor? Do you have, for example, an appropriate door between the ground floor and the basement? Sounds like the basement is within the heated envelope. Then it must be included in the heat load calculation because the heated rooms heat this area as well. That is actually not so clever, since the heated rooms then have to be heated more in order to reach the target temperature there, because a lot of heat is lost to the unheated basement. Especially from the ground floor above and the two heated rooms in the basement. I am of the opinion that this is not the way to do it. This could also have been a reason why the creator of the thermal protection certificate entered underfloor heating there. You should ask about that again.

No, there is no door at the basement stairs on the ground floor. And otherwise, I am not aware of any special measures. How can this still be saved? I don’t need a bulky heating system just to heat a guest room and a hobby room while the temperature in the other rooms in the basement and the hallway doesn’t matter to me. I don’t know anyone who heats their entire basement. That’s madness.

That is actually not so smart, since in the heated rooms more heating is required to reach the target temperature there, because a lot of heat escapes into the unheated basement.

We'll do it like this: door closed. Ventilation is running in the basement rooms.

No one is saying that the basement rooms need to be set to 22 degrees. The heating load will not explode because of this, as your existing calculation shows. It is just window dressing to say "I won't put heating there," because in fact the area is heated, just through the floor above and the adjacent heated rooms. An acknowledgment of reality, so to speak. Utility basements are usually insulated against the ground floor. That means insulation on the ceiling and the basement corridor separated from the ground floor with an appropriate door. You can also see floor plans where the staircase from the ground floor to the basement is open and you enter an anteroom that is insulated against the cellar behind it.

So basically, I can probably save myself the effort of checking whether the 7.58 W heating load for the 304m² house or 234m² ground floor/upper floor is correct or not, right? The value seems quite okay for this size. And it is also "only" an Energy Saving Ordinance 2016 house and no more. Although the ceilings had to be reduced by a total of 20cm after the calculation was made (the building authority sends its regards), this will probably not lead to a reassessment of the relevant heating systems.

Then, as mentioned, an energy consultant will be commissioned tomorrow to calculate it.

So regarding the area, I (feel) it is totally fine.

You have already paid someone for the calculations, otherwise you wouldn’t have the document in your hands. If there are any questions left, direct them there.
However, I recommend you consult the energy advisor, someone who does this professionally (not a structural engineer etc., who also calculates thermal protection proofs), for your heating selection. Especially the question of whether you can live with gas + controlled residential ventilation or if you need solar thermal with gas (general contractors will just say "yes you need it" anyway). If you are already leaning towards the air-to-water heat pump, you can save yourself that.