Interior doors - Included by the general contractor are CPL interior doors

Make sure that the controlled ventilation system is properly designed. 20-30m2/ flow easily through the door gap. Completely without any special gimmicks.

The sound, however, is probably better with the solution using the frames! Or not?

You always have the gap at the bottom. I'm not talking about specially shortened door leaves.

The frame solution is better than additional overflow elements, but anyone interested in the appearance of the door will not see it as an option. Especially if something is supposed to be flush.

Make sure the controlled residential ventilation is properly designed. 20-30m2/ flow easily through the door gap. Completely without any special tricks.

I'm relaxed about it, in our case doors are usually open and if not, it’s not a big deal. Controlled residential ventilation is highly dynamic regarding air changes/flow behavior, so I’m not worried if there is temporarily less airflow somewhere. Shortening the door leaf is a no-go for me (but you didn’t mean that either), more likely the frame variant, but most likely nothing at all and open/ajar doors. Depending on the air exchange rate, 20-30cbm/h through the normal gap can be tight, for example a larger bedroom with double occupancy and a high, desired air exchange rate. A small guest bathroom with 3sqm x 2.6m and complete air exchange every 15 minutes (humidity, OLF) already involves considerable volume. You would have to be careful that it does not pull air under the door (gap).