If people are in my chat and streaming, I'd like to know. Maybe let the streamer who owns the chat turn it on or off, but I'd like to know if people are in my chat and streaming.

I actually don't think this is a great idea. I think if you're in someone's chat, you shouldn't be there with the intention to promote your stream and "steal" viewers from whomever's chat you're in. I personally find it rude when someone says they're currently live, or about to go live, when they're in my chat. It's like asking their community to go watch them instead. There are better ways to grow.

A red circle around their icon would be a better option, but I am not sure of the usefulness of this. I would appreciate it if you could explain your reasoning behind this so I can better understand your point of view :D