Update the live MCP connection snapshot and re-render.
The constructor only receives a snapshot of the app's connection
state, so a manager opened while a connection is still settling would
otherwise keep mcp_connecting=True forever — suppressing, for
session-loaded plugins that declare MCP servers, both the "connected"
indicator and a legitimate "run /reload" hint until the modal is
closed and reopened. The app calls this whenever a connection attempt
settles — ServerReady or a startup failure, including reconnects —
so the open manager reflects the final connection state.
