My previous solution still works, but you might lose the changes (symlink) when Opera gets updated. At least that happened in my case. Applying the solution manually every time is a pain.
You can use this handy script to fix ffmpeg support for you, whenever it gets broken.
Fetch the always up to date script from here, or simply use this command to directly download the script:
curl -fsSL https://gist.githubusercontent.com/xZero707/ff2d5a76544c84e33086ed94092c0263/raw -o opera-fix-ffmpeg.sh
Remember: When downloading the script from the internet, it is always a good idea to inspect the script first.
sudo /bin/bash opera-fix-ffmpeg.sh
sudo /bin/bash opera-fix-ffmpeg.sh /path/to/your-opera-installation
The script will install or update snap chromium-ffmpeg and create symlink to latest bundled ffmpeg.so, in your opera directory.
Note that sudo is required.
Tested and working on Linux Manjaro. Should work for other Linux distros as well.
Disclaimer: This script is provided as-is. Use at your own responsibility.