feat(diag): E2EE investigation kit for the KE-1→4 cluster

LOTUS_E2EE_INVESTIGATION.md: per-KE capture runbook (console signatures, synapse
log greps + SQL against the documented LXC deployment, the KE-1⇒KE-2 causality
decision tree, ranked remediations incl. what a crypto-store reset wipes; SDK
finding: stable 41.6.0 has no OTK fix over our RC pin). Client: capture-only
console ring buffer (cryptoDiagLog, KE-signature-matched, max 200) + a Crypto
Diagnostics card in Developer Tools with a download-report button. ClientRoot
installs the capture hook at module load and mounts useSessionSync (cross-tab
sessions, prior commit).

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

src/app/pages/client/ClientRoot.tsx

@@ -43,8 +43,15 @@ import { stopPropagation } from '../../utils/keyboard';
 import { SyncStatus } from './SyncStatus';
 import { AuthMetadataProvider } from '../../hooks/useAuthMetadata';
 import { getFallbackSession, removeFallbackSession } from '../../state/sessions';
+import { useSessionSync } from '../../hooks/useSessionSync';
+import { installCryptoDiagLog } from '../../utils/cryptoDiagLog';
 import { AutoDiscovery } from './AutoDiscovery';
 
+// Capture-only E2EE diagnostics ring buffer (KE-1→4 signatures) — installed at
+// module load so it sees crypto warnings from the very first sync. Idempotent;
+// report download lives in Settings → Developer Tools → Crypto Diagnostics.
+installCryptoDiagLog();
+
 function ClientRootLoading() {
   return (
     <SplashScreen>
@@ -178,6 +185,9 @@ export function ClientRoot({ children }: ClientRootProps) {
   );
 
   useLogoutListener(mx);
+  // Cross-tab session sync: another tab logging out / in (access token changed
+  // in localStorage) reloads this tab so it never runs with stale credentials.
+  useSessionSync();
 
   useEffect(() => {
     if (loadState.status === AsyncStatus.Idle) {