Then switch to another tab — the badge stays on this app's tab. That is its whole point: it works while nobody is looking.

Nothing yet. Send a message, add a tag, or switch conversations — events this app is subscribed to appear here as they happen.

Drafts land in the reply box for the agent to edit — a mini app can never send on its own.

Writes the same store as the filter UI — watch the list and the filter chips react, then clear from either side. Tag filters accept names ("vip"), and the advanced-filter DSL resolves through the same server path as the dialog.