My version. The hole is there to sense atmospheric pressure, and to use this pressure differential between the regulator set point and atmospheric pressure. The high pressure side of the regulator varies between fill pressure (250 bar) down to regulator set pressure (say, 125 bar). Without a constant differential the regulator set pressure would vary wildly. But since atmospheric pressure is a relative constant (less than 1 bar variance), and the low pressure side (regulator set pressure) is compared to atmospheric pressure, it opens and shuts the valve/seat to maintain that constant differential that is set unless changed by the operator.
At least that’s the way I understand it from my nuclear power days in the Navy...