Install ffmpeg from RPM Fusion repo.

I installed ffmpeg from RPM-fusion-free by uninstalling the version from the update repo, but dnf now gives the following output:

Problem 1: cannot install the best update candidate for package ffmpeg-libs-6.0-6.fc38.x86_64
 - nothing provides libopenh264.so.7()(64bit) needed by ffmpeg-libs-6.0-11.fc38.x86_64 from rpmfusion-free-updates
Problem 2: package libavdevice-6.0-11.fc38.x86_64 from rpmfusion-free-updates requires ffmpeg-libs(x86-64) = 6.0-11.fc38, but none of the providers can be installed
 - cannot install the best update candidate for package libavdevice-6.0-6.fc38.x86_64
 - nothing provides libopenh264.so.7()(64bit) needed by ffmpeg-libs-6.0-11.fc38.x86_64 from rpmfusion-free-updates
Problem 3: package ffmpeg-6.0-11.fc38.x86_64 from rpmfusion-free-updates requires ffmpeg-libs(x86-64) = 6.0-11.fc38, but none of the providers can be installed
 - cannot install the best update candidate for package ffmpeg-6.0-6.fc38.x86_64
 - nothing provides libopenh264.so.7()(64bit) needed by ffmpeg-libs-6.0-11.fc38.x86_64 from rpmfusion-free-updates

I checked Firefox and videos now work. I leave the question open until I do further testing.

It appears that you already know it's not a browser issue, similar to this issue. https://support.mozilla.org/en-US/questions/1419631#answer-1593617

Can you provide a link to the video screenshot you posted so that I can test it?