This isn't exactly what I'm proposing since it seems to be based around sharing my code. I may be misunderstanding the documentation and examples however. Live Share appears to be me inviting people to connect to my personal session.

I see a codespace as a shared destination. It lives independently of any individual. I can hop in and out whenever I want and it continues to live.

To expand on this, it reminds me of how way back in the day we used to use MSN Messenger (and then Skype) to facilitate work chat. The model there was a contact list, a list of individuals I could reach out to and connect. There were group chats as well, but the primary mental model was closer to a phone call. Then Slack came and changed the model so that channels were the default, shared spaces were preferred over personal chats or ad-hoc groups. I don't want the default to be "I have my session and may invite others to join". I want the default to be "there is a shared workspace I connect to that others might be currently active in".

You might even imagine an interface similar to Slack channels (or Teams if that is your world). I could have multiple codespaces as channels that I can switch between. Within each codespace there may be active several devs. I can jump in and out. You could even setup permissions like "read only" spaces or whatever.

There is 'Discussions' for this, which you can enable per repo on GitHub, and have a sort of chat / forum as part of the repo