Excellent, thank you very much for the answer. This is exactly what we were looking for. The server way seems like the best experience for everyone.
With the limitations I think that we could even go with just the extension PubSub - is it this one ? PubSub | Twitch Developers
So we could go with architecture:
game <–> our servers
our servers → <our_message> → Twitch PubSub → Extension (viewers)
Question to the pubsub, if we broadcast a <message> at timestamp 00:20 and a new viewer joins the streamer at 00:25 does he automatically loads the latest <message>?
Btw the PubSub way would be awesome as it would require really low amount of resources on our side regardless of the amount of viewers.