How does the automatic brightness settings work? Maybe a dumb question, but I couldn't find any official documentation to confirm.

Does it use the light sensor? Do most devices support it?
Yes, it uses the light sensor, and yes most of the smartphones support it.

As for how does it work;

Smartphones, generally, have a light sensor located in the bezel right next to the screen that measures the ambient light together with control software that appropriately raises or lowers the screen brightness based on the measured light level. If you are watching in the dark the screen should be appropriately dim. When the ambient light level is higher the screen needs to be made appropriately brighter for two reasons: because of glare from ambient light reflected off the screen, which washes out the image, and because the eye's light sensitivity decreases substantially as the ambient light level increases.