With us, it is generally solved differently for the necessary circulation for the residential ventilation. The doors have a maximum of 3-5mm of air at the bottom, but the door frame at the top inside is invisibly specially milled from the factory on both sides.
We initially also had a door fitter/seller who wanted to solve it similarly to you – with about 1 - 1.5 cm of air. He was sent away immediately. But 2.5 cm is absolutely not acceptable and is technically certainly not necessary.
Ask the manufacturer of the ventilation system what they recommend or what is technically necessary. Then go to the builder with that. He should please order new door leaves right away.