Group chat doesn’t store history, so you need to be there to receive it. No history has ever been stored when you’re not in group chat, and it’s unlikely that this will change. Twitch hasn’t modified group chat at all since its launch, and many parts of it have now aged and broken. I would assume it to likely be removed at some point given that nobody hardly uses it. If you’re looking for a group chat program, many people are now using Discord.