Looks like you're trying to reinvent some wheels there.
No harm in doing so but just so you know, React (or my preference, a tinier version called Preact) would let you update new chat contents without blowing away all the other InnerHTML content. The way you're doing it now will result in a flicker, and mess with things like highlighted text will unhighlighted when replaced. And that's just with the basic dumping of the chat text into a DOM innerHTML. I'm pretty sure what you're doing there would also be susceptible to XSS without additional filtering.