Attaching a motorized flip down tv mount to my apartment ceiling
I like that mount.
It appears your soffit housing the duct work is made of steel studs covered in drywall.
This is a challenge for the weight of large TV, especially a hanging one that moves.
I would mount a Thick, long, wide board to the drywall spanning  3  studs. The board or boards need to be wider than the depth or length of the mounting plate of the the TV mount.
I would use Toggler anchors to attach the board to the studs, the toggle would/must go through the wall of the metal studs, at least 2 if not 3 anchors per stud.
You need to know exactly how the soffit is constructed, I.E. where the studs are and make sure you are mounting to them and not just drywall.
Here is good YouTube video of how to install the toggler toggle anchors.
Once you have a good solid board installed you have something strong enough to mount you TV too.
Before you install your board you should determining where the TV mount will be located and mark the location of the plate and the holes for the mounting bolts on the board.
Since it is a hanging mount i would not use lags or screws but instead i would use machine bolts into T-nuts.  Pre-drill your holes and mount the T-nut on the back side of the board. You will need to size the bolts, washers and T-nuts to work with your TV mount holes.
Here is a good YouTube video on T-nuts.