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It is force, not pressure, that determines the performance of a screwdriver. Pressure is force per unit area. Area is not relevant to the forces that are applied while using a screwdriver.
You must apply sufficient axial force, to prevent the screwdriver from being rejected by, and disengaging from the screw head. The axial force required, will depend on the torque being applied, and the head profile of the screw. A worn screwdriver will require greater axial force to deliver the same torque.
You must apply sufficient radial grip force, to prevent the handle sliding with friction against your hand. Your grip of the handle limits the torque that can be applied.