I think I read that fedora is removing the h264 and h265 codecs from their repo.
Since that is at least partly related, disabling of the codec may be a result of that decision by fedora.
You did not give us any info about your hardware and it may not be related at all since a codec is either supported or not and is responsible for managing the file formats for audio/video files. The drivers are responsible for managing hardware acceleration on devices, and if hardware acceleration is not enabled then software acceleration is necessary and video playback becomes CPU intensive.
Please post the output of inxi -Fzxx so we can see the hardware and drivers involved.
Another thought.
Since the OpenH264 codec is provided by Cisco and has been installed automatically by fedora for some time, is it actually installed on your machine?
This is what I see on my F36 machine.
# dnf list installed openh264
Installed Packages
openh264.x86_64 2.3.1-1.fc36 @fedora-cisco-openh264
sudo dnf list installed mesa
If you have mesa-va-drivers, you may want to swap them for mesa-va-drivers-freeworld.
If you don’t have rpmfusion-free-updates-testing enabled you will need to enable it.
Regarding the High CPU Usage with firefox:
The Fedora mesa package dropped support for those codecs here
The folks at rpmfusion have built mesa vaapi drver package that supports these codecs :mesa-va-drivers-freeworld it’s available but still in the update-testing repository of rpmfusion. This is also referenced in your original post, Firefox using more CPU while playing videos - #14 by ozeszty
i really say droping that hardware video accelerated driver for mesa seems strange but it shoud be asked like fedora ask on first boot up that do you want third party codec support then tap this so syaten just enable that and install.
Since this is a licensing issue with mesa and fedora dropped that then it seems not a fedora issue but rather a mesa issue. Maybe addressing it with them would have more and better affect. Without permission fedora cannot directly include that codec in what they distribute.