The Air Assault units belong to the Ground Froces, using the BMP-3 is logical.
Also the Air Assault dudes will mostly fight like usual Ground Forces and only
occasionally be delivered by helicopters. In that case it doesn´t matter if you
use the BMD-4M or the BMP-3 because the won´t use such vehicles in these
circumstances. Or if they do they need a Mi-26, which should be able to haul
the BMP-3.
Also the Air Assault dudes will mostly fight like usual Ground Forces and only
occasionally be delivered by helicopters. In that case it doesn´t matter if you
use the BMD-4M or the BMP-3 because the won´t use such vehicles in these
circumstances. Or if they do they need a Mi-26, which should be able to haul
the BMP-3.