If you're referring to VRR from the HDMI 2.1a FRL spec (used by eg. OLED TVs), then that is currently only supported for Nvidia cards on Linux. It works with the default configuration after installing the proprietary drivers. I'm currently using this with an LG OLED TV at 4K@120Hz VRR.
For AMD cards, it is currently not supported, though it might be coming soon: https://gitlab.freedesktop.org/drm/amd/-/issues/1417#note_1988469
EDIT: Also, for Nvidia, VRR is technically used/enabled on the wire for both X11 and Wayland, but the refresh rate is locked to the max on Wayland. You'll need to use X11 for the refresh rate to actually be variable.
I primarily use Alacritty. I spend quite a lot of time running things that produce ludicrous amounts of output (eg. compiling Android from source). Out of 10 or so terminal emulators I've tested earlier this year, it was the only one that didn't use 100% CPU displaying all that output, staying in the low single digits.
I'd prefer to use Wezterm because I like its lua configuration system and the builtin pane splitting, but with my workload, I still run into issues where its CPU usage shoots to 100% and becomes non-responsive for a while. (That said, it's already a lot better than before. I try to report any issues I can reliably reproduce and Wez has been wonderful about fixing them.)