I don't know a huge amount about video encoding, but I presume this is one of those libraries outlined in xkcd 2347[0]?
[0] - https://xkcd.com/2347/
replies(5):
[0] - https://xkcd.com/2347/
[0] https://link.springer.com/article/10.1007/s11214-020-00765-9
Linux doesn't really have a system codec API though so any Linux video software you see (ex. VLC, Handbrake) is almost certainly using ffmpeg under the hood (or its foundation, libavcodec).
That being said, if you put down a pie chart of media frameworks (especially for transcoding or muxing), ffmpeg would have a significant share of that pie.