Drop the last two timers: prefetch and the UI stats poll go event-driven

Phase 2.5 — `prefetch_loop` no longer wakes every 30s. It subscribes to
`MailStore::subscribe()` and only catches up missing bodies when the
generation counter ticks (event-bus delta, sync_folder finishing,
bootstrap). When the store is quiet — every cached mail has its .eml on
disk — the loop sleeps indefinitely on the watch channel. The
`PREFETCH_INTERVAL` constant is gone.

Phase 2.6 — the dashboard 1s `setInterval` is gone too. `BridgeHandle`
gets a `stats_dirty_tx: broadcast::Sender<()>` that pulses on every
`MailStore` bump, every `WsState` transition, and the start / stop
status transitions. A small watcher task inside `start()` plumbs the
two `watch::Receiver`s into the broadcast. The Tauri layer
(`stream_stats`) subscribes via `BridgeHandle::subscribe_stats()`,
takes a stats + status snapshot on every pulse (and once at startup),
and emits two events `bridge://stats` / `bridge://status` to the
webview. The React hook replaces `setInterval(refresh, 1000)` with two
`listen()` subscriptions; the initial `refresh()` still seeds the
state for the first frame.

Backend now has zero `time::sleep`-driven polling loops: the syncer is
driven by Phase 0 + bootstrap + the event bus, prefetch is driven by
store changes, and the UI is driven by pushes. The only remaining
delays are throttling (`INTER_FOLDER_DELAY`, `INTER_REQUEST_DELAY`)
and reconnect backoff, which are not polls.

166 bridge lib tests, full workspace builds, UI tsc clean.

src-tauri/src/main.rs

@@ -18,6 +18,7 @@ fn main() {
 
     let handle = BridgeHandle::new();
     let log_rx = handle.subscribe_logs();
+    let stats_rx = handle.subscribe_stats();
     let shared = Arc::new(Mutex::new(handle));
 
     tauri::Builder::default()
@@ -40,6 +41,12 @@ fn main() {
                 stream_logs(app_handle, log_rx).await;
             });
 
+            let app_handle = app.handle().clone();
+            let stats_state = app.state::<BridgeState>().inner().clone();
+            tauri::async_runtime::spawn(async move {
+                stream_stats(app_handle, stats_rx, stats_state).await;
+            });
+
             let state = app.state::<BridgeState>().inner().clone();
             tauri::async_runtime::spawn(async move {
                 auto_start(state).await;
@@ -75,6 +82,36 @@ async fn auto_start(state: Arc<Mutex<BridgeHandle>>) {
     }
 }
 
+async fn stream_stats(
+    app: tauri::AppHandle,
+    mut rx: tokio::sync::broadcast::Receiver<()>,
+    state: BridgeState,
+) {
+    use tauri::Emitter;
+    // Emit a single snapshot covering both bridge status and stats. Status
+    // transitions (start / stop) and stats changes (new mail, ws state) all
+    // pulse the same channel, so the UI replaces its periodic poll with one
+    // listen per topic.
+    async fn emit_snapshot(app: &tauri::AppHandle, state: &BridgeState) {
+        let handle = state.lock().await;
+        let status = handle.status().await;
+        let stats = handle.stats().await;
+        drop(handle);
+        let _ = app.emit("bridge://stats", &stats);
+        let _ = app.emit("bridge://status", &status);
+    }
+
+    emit_snapshot(&app, &state).await;
+    loop {
+        match rx.recv().await {
+            Ok(()) | Err(tokio::sync::broadcast::error::RecvError::Lagged(_)) => {
+                emit_snapshot(&app, &state).await;
+            }
+            Err(tokio::sync::broadcast::error::RecvError::Closed) => break,
+        }
+    }
+}
+
 async fn stream_logs(
     app: tauri::AppHandle,
     mut rx: tokio::sync::broadcast::Receiver<String>,