fix(server,app,desktop): route in-app notifications by presence cascade

Replaces the per-client stale/visibility policy with one shared
presence cascade so a backgrounded Firefox tab can no longer steal
in-app notifications from an active Electron desktop window.

Server (`agent-attention-policy.ts`): exports `PRESENCE_THRESHOLD_MS`
(3 min) and `computeNotificationPlan({ allStates, agentId, reason,
nowMs })` returning `{ inAppRecipientIndex, shouldPush }`. Cascade:
focus suppression requires presence; otherwise the most-recent
present client wins (lower-index tiebreak); push fires only when no
client is present, and never on `error`. `broadcastAgentAttention`
calls the policy once per event.

Electron (`daemon-manager.ts`, `idle.ts`): registers
`desktop_get_system_idle_time` returning `powerMonitor
.getSystemIdleTime() * 1000`. Renderer wrapper
`getDesktopSystemIdleTimeMs()` is best-effort: rejected IPC, null,
NaN, Infinity, or negative values return null without throwing.

Hook (`use-client-activity.ts`): Electron-only effect polls every 5s
and updates `lastActivityAtRef` only forward, so OS-wide activity
keeps a backgrounded Electron window present while in-window events
still update immediately.

`ClientHeartbeatMessageSchema` is unchanged; old/new clients and
daemons remain wire-compatible.

Tests: 52 focused tests across policy unit, dispatch, e2e, hook,
desktop wrapper, and permissions. Phase-3 dispatch test +
Phase-5 stale-poll test verified by mutation (breaking the focus
check / the `>` guard makes the exact regression fail).

packages/app/src/hooks/use-client-activity.ts

@@ -1,10 +1,12 @@
 import { useEffect, useRef, useCallback } from "react";
 import { AppState } from "react-native";
 import type { DaemonClient } from "@server/client/daemon-client";
-import { isWeb, isNative } from "@/constants/platform";
+import { getIsElectron, isWeb, isNative } from "@/constants/platform";
+import { getDesktopSystemIdleTimeMs } from "@/desktop/electron/idle";
 
 const HEARTBEAT_INTERVAL_MS = 15_000;
 const ACTIVITY_HEARTBEAT_THROTTLE_MS = 5_000;
+const DESKTOP_IDLE_POLL_INTERVAL_MS = 5_000;
 
 interface ClientActivityOptions {
   client: DaemonClient;
@@ -130,6 +132,31 @@ export function useClientActivity({
     };
   }, [maybeSendImmediateHeartbeat, recordUserActivity, setAppVisible]);
 
+  // Track OS-wide activity in Electron so backgrounded desktop windows still report presence.
+  useEffect(() => {
+    if (!getIsElectron()) return;
+
+    let disposed = false;
+    const pollSystemIdleTime = async () => {
+      const systemIdleMs = await getDesktopSystemIdleTimeMs();
+      if (disposed || systemIdleMs === null) return;
+
+      const systemLastActivityAtMs = Date.now() - systemIdleMs;
+      if (systemLastActivityAtMs > lastActivityAtRef.current.getTime()) {
+        lastActivityAtRef.current = new Date(systemLastActivityAtMs);
+      }
+    };
+
+    const interval = setInterval(() => {
+      void pollSystemIdleTime();
+    }, DESKTOP_IDLE_POLL_INTERVAL_MS);
+
+    return () => {
+      disposed = true;
+      clearInterval(interval);
+    };
+  }, [client]);
+
   // Send heartbeat on focused agent change
   useEffect(() => {
     if (prevFocusedAgentIdRef.current !== focusedAgentId) {