You shouldn’t have users communicating directly with anything running on the Streamers machine because then you would need for the streamer to open ports to the internet to let those connections come in, and you would also be exposing the streamers IP to users which could be a privacy violation and a security issue.
You also shouldn’t be exposing your extensions secret to anything running on the Streamers side either, which means that even if you did have users sending data to the streamer, they would have no way to verify the JWT.
Using a server to proxy data between streamer and viewers protects the streamers privacy and allows you to verify the JWT to ensure it’s legitimate traffic before sending it on to the streamer (who can connect as a client to your server, meaning they wont have to open any ports).