Sinus squeeze and reverse sinus squeeze typically indicate some kind of pathology, typically inflamed mucous membranes but sometimes anatomical obstructions like nasal polyps as has been mentioned in another thread here recently.Good description. But again, it is not just the patency of the airways leading into and out of the sinuses and middle ear; bone vs soft tissue, that requires equalization....on descent all air spaces will be subject to squeeze unless air at the ambient hydrostatic pressure is introduced into them. On a freedive descent there isn't any passive increase of pressure inside the sinuses or middle ears, hence dive diver must actively increase that internal pressure to match the hydrostatic pressure increases.
The sinuses do not always have a patent air passage as is demonstrated when a sinus squeeze occurs or worst yet a reverse block on ascent. So if a diver is always blessed with open air passage to the middle ears and all sinuses then yes on compressed gas dives the inhaled gas could passively equalize the lungs, middle ears and sinuses if the descent and ascents are slow enough. That will not work on freedives as the diver must actively pressurize those air spaces.
No big contentious issues here, just my opinion that not all air spaces can be passively equalized with increasing hydrostatic pressure increases.
The sinuses should still equalize much more easily than the ears on a free dive. You seem familiar with free diving so what follows is more for other readers than for you, but FWIW: Depending on technique, the descent rate can be much faster on a free dive than on a compressed gas dive and the available volume to equalize air spaces is less so equalization may be more effortful. Some free divers admit salt water into their middle ears and sinuses on descent, which would definitely require effort and could result in inflammation and difficulty equalizing on subsequent dives.
Best regards,
DDM