How to measure the potential gradient between large capacitor plates?
Or maybe do I place a small metal plate, have it attached to true
ground and measure the voltage?

That's somewhat close.  Remember that all voltages are relative, so there is no &quot;true ground&quot; so to speak.  Make the measurement relative to one of the capacitor plates.
You can buy an electrostatic field meter to measure the field gradient between the plates.
Another option, if you want to build a setup yourself is to place a metal probe between the plates and measure the voltage between the probe and one of the capacitor plates.

An ordinary volt meter is going to draw a few nano-amps to do the measurement.  Over time the measurement current is going to charge your probe to a different voltage.  Therefore you need a way to connect the volt meter and make a measurement quickly before the voltage drifts.
To extend the measurement time, the probe should have some capacitance relative to the plate.  The easy way to achieve this is to attach it to one of the plates through a low leakage capacitor.  Probably a plastic film type.
You need a way to connect and disconnect the probe without touching it because the mere act of touching the probe may change its voltage level.
The whole probe must be electrically isolated except for at the measurement point.  Possibly coated in rubber or some other good insulator.
With the probe relay open the tip must remain in the field for along time until the probe charges up.
Close the relay and make the measurement before the reading drifts.
You may consider buffering the measurement with an ultra low leakage op amp such as...
LMP7721
https://www.ti.com/lit/ds/symlink/lmp7721.pdf?ts=1607492515841&amp;ref_url=https%253A%252F%252Fwww.ti.com%252Fproduct%252FLMP7721
ADA4530
https://www.analog.com/media/en/technical-documentation/data-sheets/ADA4530-1.pdf