NoStrudel has an event publisher tool that lets you publish the live stream to Nostr directly.
nostr:npub1yvscx9vrmpcmwcmydrm8lauqdpngum4ne8xmkgc2d4rcaxrx7tkswdwzdu uses it each week to broadcast his owncast stream to Nostr.
Discussion
I'll have to give that another try, I used it quite a few months back and it had issues broadcasting that the stream had ended (despite telling it). Nostrudel's the main client I'm using here so will try tomorrow. Cheers.