How to determine max supportable display resolution?

The monitor sends out EDID data which contains the monitors ability list.

See here for more details.

https://unix.stackexchange.com/questions/114359/how-to-get-edid-for-a-single-monitor

How do you find out a laptop screen panel manufacturer / model with Linux? (Samsung, LG, Chi Mei, etc)

ls /sys/class/drm/
cat   /sys/class/drm/card0-DP-2/edid