The Wayback Machine at archive.org has snapshots at https://web.archive.org/web/20230000000000*/https://download.blender.org/peach/bigbuckbunny_movies/ and I was able to download a copy of big_buck_bunny_480p_stereo.ogg from there. I don't know enough about the OGG format to know if I could just use any OGG video file.
The https://www.webmproject.org/detect/ URL was working, but https://download.blender.org/peach/bigbuckbunny_movies/ is still down for me. I'll download a local copy of one of those files next time it's up.
Can't check "firefox media" test since https://download.blender.org/peach/bigbuckbunny_movies/ is down.
There are linux-firmware updates in updates-testing, including for AMD. Are those relevant?