Trying to fix/replace a ceiling light -- seen this type of mounting bracket anywhere?
That fixture was not made to use those screws; somebody rigged that by drilling pilot holes into a plastic pancake ceiling box, then used drywall screws.

They did this because the part of the fixture that was designed to attach to a ceiling box was missing. The original screws were machine thread screws and were supposed to "side screw" into the missing mating piece.

You might have some legit mounting options if there is an electrical box in the ceiling, behind that busted plastic box...