I brought this up to the Device & Sensors Working Group where the current Wake Lock API is developed: https://github.com/w3c/wake-lock/issues/84
The editor of that spec gave some input on the idea that you might find interesting / want to react to:
I think it should be a v2 thing. I'm not sure if any of the major
browsers support displaying web pages on the wearable devices such as
Android watches, or whether low power modes such as the Ambient Mode on
Android are portable between mobile platforms.
Also, the Ambient Mode is different from the usual "screen on" mode because, per Android documentation,
the application should adjust its UI specifically for this mode
(simplify the layout, remove interactive controls, reduce update
frequency etc). So in addition to opting in to be displayed in the
Ambient Mode, the web page must receive a message when the system has
entered or exited this mode.
The latter makes me wonder if a an "ambient mode" CSS Media Feature would not be at least one of the useful ways to approach this.