A digital piano only performs as the manufacturer intended if you turn it up to full volume.

For a device that includes an amplifier and (possibly) speakers, full volume is probably what the manufacturer figured would be the loudest useful volume — the point past which distortion would make it pointless to crank it any louder. Optimal audio quality would be achieved at a lower volume setting (typically 50-70%, I'm going to say with no real proof of that).

For something that has only a digital output and/or a line-level analog output (so that the primary control point for volume lies in another device later in the signal chain), a volume control, if present, is probably best left at or near 100%, unless it causes an analog output to overload the next input stage. None of this affects the "performance," though, aside from any audio engineering problems: either a weak signal causing an increased noise floor, or an excessive signal causing overload.

Very true. Touch is complex and subjective, and it involves the sound as much as the physical feeling of the keys. Adjusting the monitoring volume to match the player's perceptions and expectations is essential.

A digital piano only performs as the manufacturer intended if you turn it up to full volume.

As a rule of thumb, audio systems of all types are typically engineered to yield the best signal to noise ratio and least distortion somewhere around 70% of maximum output level. 100% is usually uncomfortably loud with a quiescent noise floor that's unpleasntly audible. I've never owned a DP with built-in speakers, but would expect that most of them would adhere to this "rule".

Or "gain" if you prefer. When digital pianos are discussed or reviewed the action and the tone are usually considered separately: but touch and tone are intimately related. A third factor, rarely discussed, is volume.
Here is a couple of provocative suggestions:

A digital piano only performs as the manufacturer intended if you turn it up to full volume.
As you turn up the volume the touch seems to get lighter. Of course it doesn't really, but the effect is real enough to affect the way we play.

Feel free to shoot me down.

  if you take p  (piano) as a middle point for reference it is about 60 db , so in normal situations, you should adapt the volume of your output device to reflect that .
Having said that , what really matters are not individual notes ,but  how different passages relate to each other in term of dynamics in a piece , so raising the volume is not going to affect the various midi velocities that you are going to have to generate if you want to respect the dynamic proportion of a given piece.
If the piece contains a wide range of dynamics ppp to ffff ( yes 4!) like In Rachmaninov concertos , you will have to use the full extent of midi values from 0 to 127 , independently of the volume of the amplifier ( if you don’t change the volume level while playing of course)

Feel free to shoot me down.

Booooo! There you go, shouted down :-)

It depends on what you are trying to do. Ultimately, you need to use your own ears and other senses to judge what works for a given piece, in a given setting, etc.

Some purists might aim to get as close as possible to an acoustic piano. Gowing down that route one might end up having to rely on objective measurements, with a decibel meter app or some such.

The general consensus, I believe, is that sitting behind the piano and at ear level, ppp is around 60dB, and fff around 90dB.

Having said that, some kind soul, who has a true acoustic, could perhaps take actual measurements and share with the rest of us here :-)

A digital piano only performs as the manufacturer intended if you turn it up to full volume.
As you turn up the volume the touch seems to get lighter. Of course it doesn't really, but the effect is real enough to affect the way we play.

Feel free to shoot me down.