Game mode requires input signal plus to be on. If game mode is enabled either automatically or by manually turning it on, input signal plus on that hdmi source will be on but greyed out so the user can't turn if off. Turning game mode off will re-enable manual control over input signal plus on that hdmi source
Transfer rate is a setting on the PS5.
My understanding is that
Auto will try and use up to and including RGB/4:4:4
-1 forces yuv4:2:2
-2 forces yuv4:2:0
So it can be used to diagnose stability/compatibility issues