carteakey.dev published a tutorial showing you how to rebuild the Mesa packages on Fedora 37 with support for the VA-API codecs.

Building Mesa from Source (with VA-API) on Fedora.

Get back HW accelerated video playback on Fedora. If you're on Fedora 37 Beta and have an AMD GPU, one of the easiest ways to get x264 hardware accelerated encoding back would be to build Mesa drivers from source. (Until we eventually get an RPM Fusion package.)

Building Mesa from Source (with VA-API) on Fedora.