From Linux, you can attempt to read the contents of the iGPU pipeline register, where it will be visible if dithering is enabled (I think it is similar to other Xe iGPUs/GPUs). And simultaneously assess the eye strain with dithering turned off. I'm not sure if Ubuntu supports new iGPUs, but you can try it anyway.
Install Ubuntu and switch the desktop environment to Xorg at the login screen. Then enable 8-bit and set Broadcast RGB to Full (there are command examples available for this https://github.com/WhisperingWindLinux/Guides?tab=readme-ov-file#how-to-switch-to-6-bit-mode). You can also enable CPU rendering by adding the following line to /.profile or /.bashrc:
export LIBGL_ALWAYS_SOFTWARE=1
Linux forces dithering to be disabled on supported Intel graphics cards, and this environment variable will switch rendering to the CPU (in theory, this might disable some post-processing).
Read the pipeline register value: https://github.com/WhisperingWindLinux/Guides/blob/main/README.md#how-to-check-if-dithering-is-present-or-not
This guide is for Ubuntu.
If more than one monitor is connected (the laptop screen may be counted as the first monitor), you can try reading additional registers: 0x71030, 0x72030, 0x73030.