I like the functionality Stadia has of an in-game messenger/chat system, however quality is terrible.
PlayStation announced of an upcoming Discord integration into their consoles. Stadia should do the same, as the quality in Discord is optimal.
@Deadline I'm not sure what kind of plan Google has with regards to Discord integration, or if it's on their radar after all.
Best thing you can do for now is submit feedback through the app to express your interest. This way the Stadia te is aware of it. The more people submitting the same feedback, the better chance it can happen.