As long as the GPU is halfway reasonable the resolution of the video has very little impact on power draw. Most of the power draw is the screen, and the fact that the CPU and GPU are active. That's one of the reasons why Intels core 100 series and up have the LP E cores in a separate tile from the regular E and P cores.

That is an interesting take. Can I save a lot of battery by choosing 1080 instead of 2/4k for laptops in general? You don't really need 2k for prose text or programming anyway.

Edit: no https://superuser.com/questions/974045/does-changing-the-screen-resolution-affect-power-consumption

on my laptop (specs wise - consider steam deck non oled, but worse graphics performance, 1080p screen (IPS)) - 5.3-6 Wh for 2x speed playback. for full hd playback 6-7 Wh. Idle power is much higher though 4.5 Wh, on my old laptop, video power consumption consumed similar power, but idle power was close to 2.5-3 Wh (in terms of specs, it had halve the number of cores, and a tn panel)