This is resonably impractical as it’s resonably impractical to get oAuth tokens for a viewer using an extension.
An Extension would first need to get permission from the user via an external window to send messages to chat.
There isn’t one
TLDR: it’s not practical to do this.
Why build an Twitch extension to send chat messages. When a user can just chat instead of click a button?
Whats the use case?