It looks like you're on the right track — Firefox is running under xwayland rather than Wayland. I had this problem with one of my devices too, but it was fixed by setting the two environment variables you mention and possibly a third, MOZ_USE_WAYLAND.

I'd start by confirming those variables work by executing Firefox with them one-shot:

MOZ_ENABLE_WAYLAND=1 MOZ_USE_XINPUT2=1 MOZ_USE_WAYLAND=1 firefox

If that works, stick them in /etc/environment or /etc/profile (or ~/.profile), restart your session, confirm they're set (eg, echo $MOZ_ENABLE_WAYLAND) and you should be good to go.

If they don't work, I'd start exploring what's preventing Firefox from running natively under Wayland.

Firefox should default to Wayland starting with version 121, this should not be needed. If you are using a flatpak for Firefox, I suggest you install Flatseal and check it it has the Wayland session toggled off. From there you should also be able to set environment variables specific to this flatpak app.