Jeweller supply houses supply small screw extractors. For these the pilot hole must be perfectly centred and perpendicular. In my experience, a quality, correct sized screw driver, well supported work and sufficient pressure will remove the screw. Holding it perfectly perpendicular to the screw is very important and be very mindful of possible slipping so you wont injure yourself or damage the laptop. Take your time and carefully think out each step.
If you have access to a drill press put the screw driver head in the chuck and using it manully (no electricity) to turn the screw driver along with the drill press’s down lever the torque will be sufficient.
In your case taking the drive and it’s caddy right out of the laptop will make all this much easier. If it is possible take out the other three screws and see if you can wiggle the drive a little bit. This can often be just enough to slightly loosen the screw. Good luck. Let us know how it goes.
For others here is Sony’s pdf of the general removal of the hard drive:
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