feat(frontend): polish web (logout, 401→pairing, reconnexion globale) (#13)

Flow logout : POST /api/logout puis retour à l'écran de pairing et
déconnexion du live. 401 renvoie au pairing sans boucle. Bannière de
reconnexion couvrant le cas live-only et le serveur indisponible.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

frontend/src/adapters/http/wsLiveClientReconnect.test.ts

@@ -190,4 +190,66 @@ describe("WsLiveClient connection state + reconnection", () => {
     expect(h.ws.getConnectionState()).toBe("closed");
     expect(h.hasTimer()).toBe(false);
   });
+
+  it("disconnect() closes and stops reconnecting but stays reusable (F6 sign-out)", async () => {
+    const h = harness();
+    h.ws.setDomainEventHandler(() => {});
+    await h.ws.ensureConnected();
+    await vi.waitFor(() => expect(h.ws.getConnectionState()).toBe("connected"));
+
+    // Sign-out: soft teardown. State is closed, the reconnect loop is dropped, and
+    // the detached socket's onclose cannot flip the state back to reconnecting.
+    h.ws.disconnect();
+    expect(h.ws.getConnectionState()).toBe("closed");
+    expect(h.hasTimer()).toBe(false);
+    expect(h.ws.needsReconnect()).toBe(false);
+
+    // Reusable: a later ensureConnected reconnects as a fresh socket (re-pairing).
+    await h.ws.ensureConnected();
+    await vi.waitFor(() => expect(h.sockets.length).toBe(2));
+    await vi.waitFor(() => expect(h.ws.getConnectionState()).toBe("connected"));
+  });
+
+  it("calls onReconnectFailed when a reconnect attempt fails (auth probe seam)", async () => {
+    const failed = vi.fn();
+    let openNextSocket = true;
+    let timerFn: (() => void) | null = null;
+    const sockets: FakeSocket[] = [];
+    const ws = new WsLiveClient({
+      wsUrl: "wss://host",
+      reconnectBaseMs: 1,
+      onReconnectFailed: failed,
+      socketFactory: () => {
+        const s = new FakeSocket();
+        sockets.push(s);
+        // First socket connects; the reconnect socket errors (upgrade rejected).
+        if (openNextSocket) queueMicrotask(() => s.onopen?.());
+        else queueMicrotask(() => s.onerror?.(new Error("upgrade rejected")));
+        return s;
+      },
+      setTimeoutImpl: (fn) => {
+        timerFn = fn;
+        return 1;
+      },
+      clearTimeoutImpl: () => {
+        timerFn = null;
+      },
+    });
+
+    ws.setDomainEventHandler(() => {});
+    await ws.ensureConnected();
+    await vi.waitFor(() => expect(ws.getConnectionState()).toBe("connected"));
+
+    // Drop the socket; the next connect attempt will fail the upgrade.
+    openNextSocket = false;
+    sockets[0].close();
+    expect(ws.getConnectionState()).toBe("reconnecting");
+    const fire = timerFn as (() => void) | null;
+    timerFn = null;
+    fire?.();
+
+    // The failed reconnect fires the probe hook and schedules another attempt.
+    await vi.waitFor(() => expect(failed).toHaveBeenCalled());
+    expect(timerFn).not.toBeNull();
+  });
 });