feat(tree): paint sidebar tree instantly from localStorage boot cache

On page reload the sidebar tree rendered nothing until every root page
was fetched (paginated), and children of expanded branches arrived even
later (breadcrumbs effect / socket connect) — the tree visibly jumped a
couple of seconds after load.

- treeDataAtom is now a facade over atomFamily(atomWithStorage) keyed
  treeData:v1:{workspaceId}:{userId} with getOnInit: true — the cached
  tree hydrates synchronously and paints on the very first render,
  together with the already-persisted open-branches map. Public atom
  interface unchanged (value or functional updater), all call sites
  untouched.
- Custom sync storage: debounced writes (500ms, coalesced, size guard,
  beforeunload flush), defensive reads (corrupted JSON -> []), no
  cross-tab subscribe (localStorage is a boot cache only).
- SpaceTree renders on cached data immediately; "No pages yet" still
  waits for the server. Once server roots merge, open loaded branches
  are re-fetched fresh and reconciled once per space (shared
  refreshOpenBranches, also used by the socket reconnect handler).
- Logout hygiene: clearPersistedTreeCaches() purges treeData:v1:* and
  openTreeNodes:* by prefix and disables further persistence (kill
  switch closes the websocket-write-vs-beforeunload-flush resurrection
  race). Wired into both handleLogout and the 401 redirectToLogin path,
  since cached trees contain page titles.
- Tests: tree-data-atom.test.ts (hydration, debounce round-trip,
  corrupted JSON, scope isolation, logout purge, persistence kill
  switch); expand-all suite adapted. 144 tree tests / full client suite
  green, tsc clean.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

apps/client/src/features/auth/hooks/use-auth.ts

@@ -23,6 +23,7 @@ import { acceptInvitation } from "@/features/workspace/services/workspace-servic
 import APP_ROUTE, { getPostLoginRedirect } from "@/lib/app-route.ts";
 import { RESET } from "jotai/utils";
 import { useTranslation } from "react-i18next";
+import { clearPersistedTreeCaches } from "@/features/page/tree/atoms/tree-data-atom";
 
 export default function useAuth() {
   const { t } = useTranslation();
@@ -122,6 +123,9 @@ export default function useAuth() {
 
   const handleLogout = async () => {
     setCurrentUser(RESET);
+    // Purge the persisted sidebar tree caches (they contain page titles) so
+    // nothing readable is left in localStorage on a shared machine.
+    clearPersistedTreeCaches();
     await logout();
     window.location.replace(`${APP_ROUTE.AUTH.LOGIN}?logout=1`);
   };