Twitch can’t help you, if they did we’d end up in the situation we have now, with “Help small streamers” and “why didn’t twitch help me”
That aside, the easiest way, is to approach broadcasters whom you think could benefit from your extension, most have business contact emails. “Hey I made this it does x I think if you install it, it will help you because of y”
One of my extensions I turned around to a group of streamers and went “hey I’m thinking of making this, it’ll do y, and it’ll help you do z” and whence I released it I wrote about it on the relevant reddit (since it’s a game specific extension)
There is no hard and fast way to promote your work, or even get people to use it. Twitch can’t really help with that, since it results in “favourtism” or overlooking of other people (which will be how the unselected people would view it)