OP, these bozos put you and anyone who walked into that room in danger. 2x4s, stacked drywall remnants, and cuts of 1-by that look like they were pulled out of a dumpster, used (basically) as pseudo furring strips/spacers!? And the "frame" they built around the ceiling perimeter (assuming they did that)... when drywall was hung on it, would cover the window trim at the top. Who does that?

While covering the ceiling will work, a better option is to take it all down to the joists and redo it the right way... or, to save time and money, take a metal spackling knife, "knock down" the popcorn texture on the ceiling, spackle divots/holes, sand, prime and paint (assuming you don't have lead paint). If you do, that's a whole other safety issue.

Man, I pray they didn't hang full span 4x8 drywall to those boards. From the look of the pic (it's hard to discern) I don't see screw holes anywhere but in the inadequately-spaced boards and in some parts of the ceiling near those boards. The drywall board weight and lack of properly-spanned support would've caused the boards to sag, buckle, and drop in no time... which seems to be what happened. I'm also surprised (or maybe not really) that there aren't any drywall screws/nails still clinging in the 2-bys, etc., due to pull-through. If they hung full-span drywall (depending on the board thickness) someone was apt to get knocked out -- or worse -- when those boards fell from ceiling height with anyone in the immediate area.

OP, sorry to say, you've been duped, scammed, hornswoggled -- intentionally or otherwise. There are nice people, with good reviews in one area of expertise, who think they know what they're doing in another because they likely watched pros, who make a craft "look" so easy. It's years of practice that get pros to where they are. You pay for that honed skill set. Any knucklehead can go to a box store and pick up drywall boards, screws, tape, and compound. Nice (or not), well-reviewed (or not) these designer/"installers" were negligent in every sense of the word -- and were severely out of their depth here.

Get your money back. You have the pics of their shoddy "craftsmanship." Threaten a lawsuit if they refuse to reimburse you the full amount, because now you'll have to pay someone to undo what they did just to fix it the right way.

After getting your money back, hire a licensed and insured contractor who knows what they are doing and has references that can speak to past success with the same type of work you need done... not another interior designer.

Based on the pic, I wouldn't even trust these folks to hang a ceiling lamp, let alone amend a ceiling.

Good luck, truly.