Self tapping screws work but then the issue will be the gate frame material will wallow out and you will lose the screw if you’re lucky and or the frame will collapse if you’re not.
I would drill through the hinge bracket and gate frame and install a bolt and nut. Make sure everything is tight, original bolt and clamp, and the new bolt because if you don’t you will have a wallowing out issue.
The best answer is to have a welder change out the 16 gauge gate frame upright for one made with schedule forty pipe.