Difference between apartment door & soundproof door

because of the controlled residential ventilation. There must be a gap of at least 1 cm under the door for ventilation.

I have thought about that too.

Does this also apply if there is no valve (supply and/or exhaust air) in the storage room?

There should be a valve (outlet/inlet) in every room, including the freezer/utility room.

We do not have soundproof doors and also do not find it practical in an average house, where you always hear outdoor noises a bit through windows, exterior walls, and the front door anyway. Of course, you can do it, but it is a cost factor that, in my opinion, is unnecessarily spent.
However, I don't know what else you have installed – especially between the individual residential units, the priority must rather be on soundproofing.
What good are great doors inside the residential unit if you hear the neighbors through the walls or ceiling? You are usually not as sensitive to your own noises as to noises made by others.
The controlled residential ventilation itself is quite dominant in terms of noise level. When the door to the freezer room is open, it annoys me. My husband leans the door shut briefly, I go and close it. You can sometimes hear the airflow in the ducts as well, but not during everyday noises, radio, and daily work sounds.
Regarding washing machines and dryers, I agree with the others: what should disturb there?
Important, I think, is good planning of the rooms, e.g. the technical rooms stacked or adjacent and not in contact with the living rooms of the other residential units.
Regarding point 1, I cannot say anything.

Thank you all very much for the hints.

Most likely you are right. I am overthinking small things. Therefore, I would exclude the topic of "soundproofing" and get regular doors.

So far, I had Westag / Getadoor doors with CPL in mind, even though painted doors look better in terms of surface. How would the doors from Prüm or Hori (Holz-Richter) compare to Westag? With Hori, there are already flush internal doors that cost around 600€.

Addendum: The Hörmann interior doors (manufacturer probably Huga) are also extremely cheap compared to other manufacturers. The only disadvantage: Also extremely long delivery times of up to 2-3 months.