They're using a torque screwdriver, which ensures tightening to a specified torque to prevent excessive tightening. The "clicking" is made by the clutch that disengages once the preset torque has been reached.

> Probably a dumb question, but what are the 3 taps for after screwing each screw? I presume they are tapping the screwdriver itself?

I think it’s a torque screwdriver.

It’s a torque screwdriver as others have said but to me it made the whole video into an asmr experience.