fix(pet): each user's pet tells only of their own sessions

An admin/analyst's pet counted every user's sessions (live, waiting, errors)
because their WebSocket carries everyone's. Server mode now marks their
session/agent/event frames `mine: true|false` (scope.broadcastAudience owners,
worked out once per broadcast), and GET /api/sessions?mine=1 lists only the
caller's own sessions (ownSessionWhere). The pet seeds from mine=1 and skips
frames marked mine: false. Developers and local mode are unchanged.

client/src/components/Sagi/__tests__/Sagi.test.tsx

@@ -200,6 +200,20 @@ describe("Sagi widget", () => {
     expect(within(liveChip).getByText("2")).toBeInTheDocument();
   });
 
+  it("counts only the viewer's own sessions (another user's arrive marked mine: false)", () => {
+    renderSagi();
+    act(() => {
+      eventBus.publish({ ...sessionMsg("mine", "active"), mine: true });
+      eventBus.publish({ ...sessionMsg("theirs", "active"), mine: false });
+      eventBus.publish({ ...sessionMsg("theirs-err", "error"), mine: false });
+    });
+    fireEvent.click(screen.getByRole("button", { name: /open sagi companion/i }));
+    const panel = screen.getByRole("dialog", { name: /chat with sagi/i });
+    const liveChip = within(panel).getByText("live").closest("span.rounded-full")! as HTMLElement;
+    expect(within(liveChip).getByText("1")).toBeInTheDocument();
+    expect(screen.queryByText(/theirs/)).toBeNull();
+  });
+
   it("respects the enabled preference", () => {
     localStorage.setItem("agent-dashboard-sagi-enabled", "false");
     renderSagi();

client/src/components/Sagi/useSagiBrain.ts

@@ -7,7 +7,8 @@
  *   burst of the same event into one count), the pet's one-shot animation
  *   "moment", and imperative controls (mute, clear alerts, pat, set thinking)
  *   for the UI shell. It also greets once per browser session and makes an
- *   idle pet fidget now and then.
+ *   idle pet fidget now and then. It only ever counts the viewer's OWN sessions
+ *   (`mine=1` seed, and frames marked `mine: false` skipped).
  * @author Nguyễn Ngọc Trí Vĩ <vinnt@smartgift.vn>
  */
 /* =============================================================================
@@ -278,7 +279,7 @@ export function useSagiBrain(): SagiBrain {
       }, GREET_DELAY_MS);
     };
     api.sessions
-      .list({ status: "active", limit: 100 })
+      .list({ status: "active", limit: 100, mine: true })
       .then((res) => {
         if (cancelled) return;
         update((prev) => seedSessions(prev, res.sessions, Date.now()));
@@ -294,6 +295,9 @@ export function useSagiBrain(): SagiBrain {
   // Subscribe to the live stream and connection status.
   useEffect(() => {
     const unsubMsg = eventBus.subscribe((msg: WSMessage) => {
+      // Each user's pet tells only of their own sessions: an admin/analyst
+      // gets every user's, marked `mine: false` when not theirs.
+      if (msg.mine === false) return;
       const prev = stateRef.current;
       const { state: next, pulse, subject } = reduceSagi(prev, msg, Date.now());
       // Most frames only move lastActivityAt, which the moods read at a 1 s