I am running F33 with mesa git and my 6700XT works pretty well apart from some minor graphic glitches. I thought they come from mesa git but the version from the repos suffer from the same behaviour.
After you’ve put the firmware into the right location you’ll need to run
sudo dracut -f but keep in mind that that command will only rebuild the inintrd from the kernel you’ve just booted with.
To check whether it worked do a
sudo lsinitrd | grep "navy_fl". If this command doesn’t produce any output you did something wrong, but if not you’re all set.