One of the “modern, space saving” types of elevator installation today are where the driving machine is indeed located inside the top of the elevator shaft either rear center or side mount verses on the roof in an enclosed room.
The noise you hear is indeed the brake snapping open and dropping closed.
Unfortunate for you, that driving machine is probably about ceiling height or a little higher and as noted, mounted on your side of the shaft way wall. Those noises we hear in the video have nowhere to go but out into your lobby which is right outside your front door. And yep….it’s loud.
Might the noise level be reduced by brake adjustments? Maybe maybe not.
Should there have been a disclosure to a prospective buyer on this annoying noise? Good question.