Derailleur-shifters compatibility Shimano GRX

The rear pull ratios used by Shimano are:

1. SIS v1 for Dura-Ace 7400 only, which was about 1mm cable to 1.9mm derailleur movement
2. SIS v2 for everything excluding that, up to the introduction of 10-speed MTB (i.e. including 10-speed road, which came before 10sp MTB), which was about 1:1.7
3. Dynasys / 'New MTB' - which was introduced for 10-speed MTB and kept for 11 & 12-speed, which is about 1:1.2
4. 'New Road', which was introduced for Shimano 11-speed road, and subsequently used for all 10-speed road (which includes gravel) products introduced since the introduction of that, which is about 1:1.4

Essentially with ever more closely spaced sprockets, it emerged that while pulling less cable means a shift requires more force, it makes shifting more accurate/precise/easier to setup. Hence after the introduction of 10-speed MTB which pulls more cable per shift, and the introduction of hidden cabling for second-generation 10-speed road, which adds more right-angles/friction, Shimano came up with an intermediate shift ratio between MTB and the previous standard. Since the old ratio didn't work that well with hidden cabling & 10-speeds or more, they essentially have one standard that is used for all new 10 & 11-speed, and probably will be kept for 12-speeds as well.

So the RX812 is not '11-speed', since the RD is not indexed. It will work with shifters that use Shimano's new road pull ratio, which is anything GRX (10 or 11-speed), anything 11-speed, and Tiagra 4700 10-speed.

There are some older 10-speed road shifters using the standard-for-everything-for-a-quarter-of-a-century-pull ratio, but they are no longer in the Shimano range.

The thing specifically with RD-RX812 is it's marked for a 1x drivetrain, and Shimano don't have 1x levers for road (only for gravel), so they only show it compatible with the GRX levers, since these have brake-only levers. There's however nothing stopping you using it with, say, SL-4700-R, which is a flat bar 10-speed lever, and a Deore 10-speed 11-42 cassette.

The Shimano compatibility documentation gives the official answers

The RD-RX800 is compatible with all the 11 speed road shifters

The RD-RX812 is compatible with GRX levers only, but that is because the RX-RX812 is for 1x setups, only the GRX range has 1x levers, with the left unit being a brake lever only.

Note that although both the 800 and 812 derailleurs expect the cable pull length from an 11 speed shifter the 812 actually has a slightly different actuation ratio than the 800, because it is designed to be used with mountain bike wide range cassettes, which have different sprocket spacing that road cassettes.

Shimano does not publish any information for compatibility between road (including gravel) and MTB shifters and derailleurs. It's generally understood that mixing road and MTB group components does not work.