However I've just found something under Settings - Accessibility that might mitigate the problem a little more. Extra dim: dim screen beyond your phone's minimum brightness.
It still won't really be off though, most likely.
And the text labels on these settings belong in a Monty Python sketch about product management.
Pressing the physical button used to work, even with the current oddball settings. It only stopped being effective a few weeks ago, when using a wireless charging stand.
It still works when I switch back to USB charging. Presumably because it would be too easy to simply place the phone face down, effectively revealing user preference.
When enabled, it seems to have two options to either enable "when charging" or "when docked and charging". I wonder if your wireless charger is considered a dock and hence activates this different mode than you get for regular USB charging.
Pixel 6, US, I keep it up to date.