FLV is a relic of the Flash era: the format YouTube grew up on, stranded when Flash died. It was born in 2002, Macromedia (later Adobe), for Flash Player, and its real weak spot is playing anywhere at all since Flash was switched off in 2020.
WEBM is video the way browsers like it: open, royalty-free and built to stream. A Matroska-based container restricted to VP8/VP9/AV1 video with Vorbis or Opus audio. That makes it the right destination when what you need is embedding on the web without licensing worries.