I thought that there was VRR support over HDMI even for versions below 2.1 spec.
Yes, there is FreeSync HDMI, which is supposed to be supported on Linux, and which is unrelated to HDMI 2.1 VRR. Don’t see anything about the monitor supporting that though (LG 24GS60F based on your previous post). Nor anything about HDMI 2.1 VRR, it probably only supports VRR via DisplayPort Adaptive Sync.
Apparently so it does, and it says “HDMI Freesync” rather than “HDMI [2.1] VRR”. FreeSync HDMI is a completely different protocol and is supposed to work under Linux. Found a thread here, can you try
cat /sys/kernel/debug/dri/0/HDMI-A-1/vrr_range
andedid-decode < /sys/class/drm/card0-HDMI-A-1/edid
? Though there is no solution there.