Ignoring fireproofing, because currently there is none... I'd go with the "make the wall taller" option. Since the drywall was painted without any mud on the screws, and considering the "industrial" setting, let's go with "not too ugly, but still quick and dirty" solution.
If the drywall is just "flapping around" and the wall is connected to the ceiling via studs that are out of frame in the picture:
Get some plywood/OSB/planks, cut to width of about 20cm and length "long enough to fit behind the drywall but not too long". Insert behind drywall, and drive in the drywall screws, so the existing drywall will serve as support to hold the piece of wood behind it. The new drywall will be screwed onto this piece of wood, so it will be aligned with the old one.
Next put a drywall stud on the ceiling, fastened to the beams, right above the wall (use a straight edge) and screw some drywall sheets on both sides.
If the wall has a horizontal "stud" inside at the top to hold it together: forget about the planks, screw another stud horizontally on top, and install drywall between it and the ceiling.
You'll have to cut the drywall sheets to match the shape of the beams on the ceiling if you want it to be draft proof. It's either that, or you make a flat ceiling so you don't have to cut the walls around the beams.
Once this is done, you should have a bit of space between the drywall and the beams, because it's not possible to have a tight fit. You can fill it with mud, or just blow some expanding foam in the cavity between the two drywall sheets. Mud is likely cheaper.