Not sure if this is the place for hardware repair stuff, but can't find a community for that, so... yeah.
It looks like the dremel slot is too wide for a screwdriver to catch on. (And also ow, marred the back panel. Not much we can do about that.)
Might try the rubber band thing? That's another trip to the store, but fortunately rubber bands are pretty cheap...
(the laptop works fine, we just want to upgrade the SSD)
-- Frost
Super small drill followed by an easy out?
If that doesn't work I think you're safely within "drill it out" territory.
Hmm. We don't actually have a drill, and it looks rather expensive (by our standards) to get one.
Poop.
But there's a makerspace somewhat nearby and I bet they have drills. Maybe they even have a screw extractor set on hand. We should pop over there.