Even if you set your phone to a lower res, on every OLED screen, battery consumption is primarily driven by its refresh rate, how bright the screen is and what colours it is displaying (black pixels are completely turned off and consume zero power). Lower resolution (software downscaling) just means the phone uses groups of physical pixels to display a single “software” pixel. Because the physical lights are still active, the hardware power draw remains nearly the same. Lower res would give you maybe 0.1% longer battery life. Lowering the resolution can help only in games.
Edit: Or to put it this way - if you lower your resolution by half, each pixel is now four times larger to cover the same screen area. Same refresh rate, same brightness, same colours being used…
