You sound like 1.125 watts is insignificant to a laptop, but my laptop idles around 6 watts and it is currently using 8 watts since I've got some stuff running. Shaving off 1.125 watts is a 14-19% improvement.
Exactly. And honestly- the screen is way way more than 1watt. According to RAPL power, a USB-PD power analyzer- changing the brightness on my 15" 4k OLED laptop screen can reduce power usage by 15-20W. The nature of OLED makes it hard to get a clear picture.
I propose the below as various factors that can be larger:
Slower fan speed because of lower ambient temperature.
Different dark/light ratio and/or adaptive screen brightness.
Wifi spectrum congestion, variable power levels to maintain proper SNR.
Wifi/ethernet- broadcast packets.
The list goes on. Most of these are below a watt, but demonstrate the point that you've got a lot more variables than just one setting in a browser.