Surface the event-bus WebSocket state in the UI

SDK (sdk-event-bus amended on the fork): a new `WsState` enum
(`Stopped`/`Connecting`/`Connected`/`Reconnecting`) is broadcast through a
`watch::Sender` inside `EventBusClient`, exposed via `state()` for
observers. Transitions are emitted at every step of the reconnect loop,
plus a `Drop` guard guarantees a final `Stopped` even on a panic in the
caller's task tree. Two new SDK tests cover the initial value and
multi-subscriber broadcast.

Bridge: capture `bus_client.state()` at start, mirror it into a serde
`WsStatus` field on `BridgeStats`, and clear on stop.

UI: add a third stat card "Realtime" with a colored dot (green Connected,
orange pulsing Connecting/Reconnecting, gray Off) reading
`stats.ws_status`. Stats grid switches from 2 to 3 columns.

Submodule pointer bumped to the rebuilt `tutabridge-integration` which
cherry-picks all six SDK branches on `upstream/master`; the move-mails
fixup (use `make_test_facade` so its test compiles alongside the blob
branch) is re-applied. 341/341 SDK lib tests pass, 154/154 bridge tests
pass.

ui/src/types.ts

@@ -9,9 +9,12 @@ export interface Config {
 
 export type BridgeStatus = "Stopped" | "Starting" | "Running" | { Error: string };
 
+export type WsStatus = "Stopped" | "Connecting" | "Connected" | "Reconnecting";
+
 export interface BridgeStats {
   uptime_secs: number | null;
   mails_synced: number;
+  ws_status: WsStatus;
 }
 
 export function statusLabel(status: BridgeStatus): string {