Some tubes like to have G2 feed with a lower voltage than B+
I mean tubes like EL500 - EL504 - GU50 - 807 .....
There are layers of misunderstanding driving this thread. Not because you don't understand tubes, but because you're looking at the 807 outside of the context of its times.
The 807 is nothing more than a 6L6G with a top cap, which means you can apply a plate voltage higher than the 6L6G's ratings and not risk arcing to another pin on the bottom of the tube. Don't give it any magic, just treat it like another 6L6 (within the limits of its ratings).
Screen (G2) voltage determines the peak plate current possible from a tube. Plate current * Load impedance determines the peak plate voltage swing possible from a tube, as long as the B+ is higher than this by some amount (the saturation plate voltage). Peak plate current * Peak plate voltage / 2 = RMS Power output.
If plate current (swing) stays the same, you can increase the load impedance and B+ to raise the peak plate voltage swing. If you notice all the 807 conditions you posted kept roughly the same screen voltage,
so the plate current capability of the tube stayed the same. But to get more power, the supply voltage and load impedance were raised. Same current swing * bigger load impedance = bigger plate voltage swing (which was allowed by higher B+) --> more output power.
But notice the tube bias is roughly the same in all the conditions... The similar G2 voltages means bias voltages remained similar.
And so did "Peak A.F. grid voltage", which is the signal input to the 807. Raising load & supply voltage while keeping G2 and bias similar yielded more output power with similar driving signal, or "better power sensitivity".
Now let's recall this is an 807, with a plate brought out to a top cap, well away from the other tube pins. As a result, the plate voltage rating is much higher, because it's less likely to arc to other tube elements at the base pins. Now you
could run this tube in class AB just as you would with a 6L6, with 350-400v on both plate and screen.
But you paid for a tube with a top cap, so the manufacturer assumes you'll want to run the 807 plate much higher than the rating for the 6L6.
When plate voltage is very high, it might not take a lot of screen voltage to get enough plate current swing for the power output you want. It would be especially handy if the screen voltage were 1/2 the plate voltage (then you could use Sluckey's method of getting 1/2 B+ for the screen, and sending full-B+ to the plate).
Hopefully you now see why it seems like when you see an 807, you see a higher plate voltage & lower screen voltage. If you weren't running the plate voltage well above screen voltage (or the 6L6 plate voltage rating of the day), it would've seemed silly in the old days to bother with using an 807 at all.
... On the 807 datasheet the spec says you must use a voltage divider (a pot) ...
What it really says is, "Don't use (just) a series resistor to get your screen voltage."
The series-resistor idea is, "I've got 500v and want 250v on my screen, and the screen current will be as high as 20mA, so let me just stick 250v/0.02A = 12.5kΩ between the plate supply node & screen to get my reduced screen voltage."
Imagine one of the preamp pentode stages you've looked at recently. Each had a cap from screen to cathode or ground, along with a series resistor from B+ to screen. This arrangement, minus the cap to ground, is using "a series resistor to set screen voltage." The screen current varies with applied voltage, so the screen voltage will vary if you do this, because there is a relatively high impedance (resistance) between the screen and the voltage source.
So stick a 20-40µF cap from the screen to ground. The cap supplies much of the varying screen current, and this starts looking a lot like an average guitar power supply (and it is exactly that, except for deriving the lower screen voltage, if needed).
You
could add a resistor to ground across the screen node filter cap, but it will create a lot of waste heat and probably won't add much stability to the screen voltage without that waste power. You could use a regulator to get the stable screen voltage, but you just transferred the waste power from a resistor to a solid-state device. The worst case with the screen node cap is that there might be a little screen voltage sag, but no more than any other guitar amp, especially if you derive the lower screen voltage as in Sluckey's method (it's a relatively low-impedance voltage source).