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.

Cargo.lock

@@ -781,7 +781,7 @@ dependencies = [
 
 [[package]]
 name = "crypto-primitives"
-version = "348.260526.0"
+version = "348.260528.0"
 dependencies = [
  "aes",
  "base64 0.22.1",
@@ -5304,7 +5304,7 @@ dependencies = [
 
 [[package]]
 name = "tuta-sdk"
-version = "348.260526.0"
+version = "348.260528.0"
 dependencies = [
  "android_log",
  "argon2",
@@ -5657,7 +5657,7 @@ checksum = "06abde3611657adf66d383f00b093d7faecc7fa57071cce2578660c9f1010821"
 
 [[package]]
 name = "util"
-version = "348.260526.0"
+version = "348.260528.0"
 dependencies = [
  "thiserror 2.0.18",
 ]

crates/bridge/src/bridge.rs

@@ -52,10 +52,32 @@ pub enum BridgeStatus {
     Error(String),
 }
 
+/// Live state of the event-bus WebSocket. Surfaces directly in the UI so the
+/// user can see at a glance whether realtime push is healthy.
+#[derive(Debug, Clone, Copy, PartialEq, Eq, serde::Serialize)]
+pub enum WsStatus {
+    Stopped,
+    Connecting,
+    Connected,
+    Reconnecting,
+}
+
+impl From<tutasdk::event_bus::WsState> for WsStatus {
+    fn from(s: tutasdk::event_bus::WsState) -> Self {
+        match s {
+            tutasdk::event_bus::WsState::Stopped => Self::Stopped,
+            tutasdk::event_bus::WsState::Connecting => Self::Connecting,
+            tutasdk::event_bus::WsState::Connected => Self::Connected,
+            tutasdk::event_bus::WsState::Reconnecting => Self::Reconnecting,
+        }
+    }
+}
+
 #[derive(Debug, Clone, serde::Serialize)]
 pub struct BridgeStats {
     pub uptime_secs: Option<u64>,
     pub mails_synced: usize,
+    pub ws_status: WsStatus,
 }
 
 pub struct BridgeHandle {
@@ -65,6 +87,8 @@ pub struct BridgeHandle {
     started_at: Option<std::time::Instant>,
     store: Option<Arc<MailStore>>,
     task: Option<tokio::task::JoinHandle<()>>,
+    /// Latest event-bus state, populated at `start` and observed by `stats`.
+    ws_state_rx: Option<watch::Receiver<tutasdk::event_bus::WsState>>,
 }
 
 impl BridgeHandle {
@@ -77,6 +101,7 @@ impl BridgeHandle {
             started_at: None,
             store: None,
             task: None,
+            ws_state_rx: None,
         }
     }
 
@@ -97,9 +122,15 @@ impl BridgeHandle {
             Some(store) => store.total_mail_count().await,
             None => 0,
         };
+        let ws_status = self
+            .ws_state_rx
+            .as_ref()
+            .map(|rx| WsStatus::from(*rx.borrow()))
+            .unwrap_or(WsStatus::Stopped);
         BridgeStats {
             uptime_secs: self.started_at.map(|t| t.elapsed().as_secs()),
             mails_synced: count,
+            ws_status,
         }
     }
 
@@ -235,6 +266,7 @@ impl BridgeHandle {
             }
         }
         let bus_ids_for_handler = bus_client.last_batch_ids();
+        self.ws_state_rx = Some(bus_client.state());
 
         let task = tokio::spawn(async move {
             let imap_tls = tls_acceptor.clone();
@@ -343,6 +375,7 @@ impl BridgeHandle {
             let _ = task.await;
         }
         self.started_at = None;
+        self.ws_state_rx = None;
     }
 
     fn emit_log(&self, msg: &str) {

ui/src/App.css

@@ -230,10 +230,33 @@
 
 .stats-grid {
   display: grid;
-  grid-template-columns: 1fr 1fr;
+  grid-template-columns: 1fr 1fr 1fr;
   gap: 12px;
 }
 
+.ws-badge {
+  display: inline-flex;
+  align-items: center;
+  gap: 8px;
+  font-family: var(--brand);
+  font-size: 14px;
+  font-weight: 500;
+  color: var(--on-surface);
+  line-height: 1;
+}
+
+.ws-dot {
+  width: 10px;
+  height: 10px;
+  border-radius: 50%;
+  display: inline-block;
+  flex-shrink: 0;
+}
+
+.ws-dot.pulsing {
+  animation: breathe 2s ease-in-out infinite;
+}
+
 .stat-card {
   display: flex;
   flex-direction: column;

ui/src/components/Dashboard.tsx

@@ -1,7 +1,21 @@
 import { useState } from "react";
-import type { BridgeStatus, BridgeStats } from "../types";
+import type { BridgeStatus, BridgeStats, WsStatus } from "../types";
 import { isError } from "../types";
 
+function wsBadge(status: WsStatus): { color: string; label: string; pulsing: boolean } {
+  switch (status) {
+    case "Connected":
+      return { color: "var(--green)", label: "Connected", pulsing: false };
+    case "Connecting":
+      return { color: "var(--orange)", label: "Connecting…", pulsing: true };
+    case "Reconnecting":
+      return { color: "var(--orange)", label: "Reconnecting…", pulsing: true };
+    case "Stopped":
+    default:
+      return { color: "var(--gray)", label: "Off", pulsing: false };
+  }
+}
+
 interface Props {
   status: BridgeStatus | null;
   stats: BridgeStats;
@@ -122,6 +136,23 @@ export function Dashboard({ status, stats, hasSavedSession, loading, onStart, on
           </span>
           <span className="stat-label">Uptime</span>
         </div>
+        <div className="stat-card">
+          <span className="ws-badge">
+            {(() => {
+              const b = wsBadge(stats.ws_status);
+              return (
+                <>
+                  <span
+                    className={"ws-dot" + (b.pulsing ? " pulsing" : "")}
+                    style={{ background: b.color }}
+                  />
+                  <span className="ws-text">{b.label}</span>
+                </>
+              );
+            })()}
+          </span>
+          <span className="stat-label">Realtime</span>
+        </div>
       </div>
     </div>
   );

ui/src/hooks/useBridge.ts

@@ -9,7 +9,11 @@ const POLL_INTERVAL = 1000;
 export function useBridge() {
   const [config, setConfig] = useState<Config | null>(null);
   const [status, setStatus] = useState<BridgeStatus | null>(null);
-  const [stats, setStats] = useState<BridgeStats>({ uptime_secs: null, mails_synced: 0 });
+  const [stats, setStats] = useState<BridgeStats>({
+    uptime_secs: null,
+    mails_synced: 0,
+    ws_status: "Stopped",
+  });
   const [hasSavedSession, setHasSavedSession] = useState(false);
   const [bridgePassword, setBridgePassword] = useState<string | null>(null);
   const [logs, setLogs] = useState<string[]>([]);

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 {