Aside from all of the critical remarks, the way to determine the minimum gate voltage required is to use the data sheet curves. Certainly reading the data sheet is indeed tedious, BUT the actual product data sheets have a whole lot of useful information, that includes very useful graphs that show (usually), resistance, or conductance, versus the gate voltage, at different temperatures.
So my very serious answer is to download the manufacturer's data sheet pages.

As for that actual circuit, my question is what is the intended application?? And why that particular circuit??
It is a power supply of some kind, and my guess is that the goal is to provide some amount of current at some voltage.
It will help some of us to provide better answers if we know what the intention actually is.

Thank you

It is a triode tube tester. The circuit is not mine so I didn´t fell free about posting it

The goal was to make a test of the circuit with low voltage just to check doesn´t blow up, but maybe apliying very low voltage could be bad for the MOSFETs.

I have made the test first with half the voltage and later with nominal voltage and worked fine

 

as with any linear regulator, power dissipated by series transistor is proportional to current and voltage drop across that transistor. this drop is greatest when its output is set to low voltage...
suppose current is 50mA. suppose output is 22V. then transistor will need to endure (sweat as heat) power Pd=50mA*(422V-22V)=50mA*400V=20000mW = 20W. transistor can handle that with ease if heatsink is large enough.

 

In a typical Tube Tester, with a simple test for "short Circuits and Leakage", the test is done with the higher voltage, a resistor, and a neon indicator to indicate current flow. Some testers differentiate between leakage and shorted circuits, with different neon indicators. The common power is the high voltage source used for the grid-control ability tesing. It must be a more complex tester to require a regulated voltage.

 

i once rewinded a secondary on transformer with a blown input fuse (removed and omitted by me)
i made a quadruple output to test it's loading capabilities

so the most power output was all secondaries in series - however that limitted the output current range signifficantly
the output was 60V DC & i used it to test DB3-s . . . at few milliamps the voltage dropped to below the DB3's barrier (27 to 34 V)
but i was able to measure the apx. breakdown voltage and some of the conduction I/V curve

the point is the 300V ~AC output is a "label" - unless you know what to do with it
++ if it's a high power one !!! you don't likely want to "short" it !!!