Old life hack that occasionally works for this is to use a rubber band. Grab a rubber band wide enough to cover the screw head, push the screwdriver into the screw through the rubber band, and pray it has enough grip to twist the screw loose. Good luck with whatever method you use.
I’ve tried it a dozen or so times, maybe worked 2-3 of them. I keep it in my arsenal of tricks because it’s quick and easy to try with no negative repercussions if it doesn’t work.