Yeah, one thing that would be cool in the future is some kind of public playback URL or HLS endpoint for each live stream.
Something simple like /stream/{id}.m3u8 that apps or websites could embed.
Not urgent, but it would open up a lot of integrations because Im also building a small streaming project for my own site, and having a simple public playback URL would make it easier to integrate external sources like yours. Nothing complex, just something that tools can read when a stream is live.