A chat application wouldn’t really make sense as an extension. Extensions can be a video overlay, a component, a panel, or mobile, all of which would be somewhat redundant for your use case as Twitch is already displaying chat so why would a streamer want to duplicate that in a panel or over their stream?
You’re right in that extensions are aimed at end users. If you want to do something to enhance chat functionality on Twitch then perhaps consider doing what FFZ or BTTV do and use a browser extension to add features to chat.