fix(auth): /auth/session must enforce session timeout symmetrically (#350 recurrence)

Third loop fix in the same /admin/login → /admin/dashboard → /admin/login
pattern as #355 and #363. Reported on v3.39.1-beta.0 — the loop returns
after a server restart or after an idle gap longer than the configured
session timeout.

## Root cause (server)

`sessionTimeoutMiddleware` is mounted on `/api/admin` (server.js:411). It
rejects with `401 SESSION_TIMEOUT` when either:
  - the in-memory `lastActivity` for the token is older than the timeout, or
  - this is the first request with this token AND the token's `iat` is
    older than the timeout (post-restart guard).

`/auth/session` lives under `/api/auth/session`, NOT under `/api/admin`,
so the middleware never runs for it. Result: an idle/old-iat admin token
returns `valid: true` from `/auth/session` while every protected
endpoint immediately rejects it with `401 SESSION_TIMEOUT`. Frontend's
401 interceptor hard-redirects to `/admin/login`, `/auth/session` says
valid again, loop closes — exact same shape as the previous two
asymmetries the symmetry pass missed.

Fix: add a non-mutating `isSessionExpired(token, decoded)` helper to
`middleware/sessionTimeout.js` that reads the same in-memory map and
applies the same lastActivity / iat-vs-timeout logic as the middleware,
without updating the map (the middleware is the only place that records
activity; `/auth/session` is read-only by design). `/auth/session`
calls the helper for `decoded.type === 'admin'` after the existing
admin-existence and password-change checks. Same try/catch fall-through
pattern as the prior fixes so a missing/broken helper doesn't fail-closed
during early bootstrap or in test stubs.

## Root cause (client race amplifying the loop)

Even with the server fix, the previous `useSessionTimeout` hook called
`AdminAuthContext.logout()` which dispatches `POST /auth/logout`
fire-and-forget AND has its own `finally { window.location.href }`,
then immediately set `window.location.href = '/admin/login?session=expired'`
on top. Two consequences:
  - The cookie wasn't reliably cleared before the new page loaded —
    if any /auth/session asymmetry slipped through, the loop replayed
    inside the same tab. New-tab and "refresh several times" "fixes"
    were just the logout request eventually completing.
  - Two redirects raced; sometimes the `?session=expired` query was
    dropped, breaking the login-page toast.

Fix: rewrite the hook to (a) await `POST /auth/logout` so the cookie
is guaranteed cleared, (b) clear `sessionStorage.admin_user` directly
instead of going through AdminAuthContext.logout (which has the
side-effect redirect we don't want), and (c) navigate exactly once
with the `?session=expired` query.

## Tests

- `__tests__/routes/authSession.symmetry.test.js` — 4 new cases under
  a `session-timeout symmetry` describe block: helper says expired →
  valid:false; helper says active → valid:true; helper not called for
  gallery tokens; helper throws → fall through to valid:true (defensive).
  Existing 9 tests still pass (mock now includes
  `isSessionExpired: jest.fn(() => Promise.resolve(false))` as the
  default).
- `__tests__/middleware/sessionTimeout.isSessionExpired.test.js` — 7
  new unit tests for the helper itself: fresh token / old-iat /
  recently-active / null-input / no-mutation / 60-min default
  boundary cases.

20 cases total, all green. Lint clean on every touched file.

backend/__tests__/routes/authSession.symmetry.test.js

@@ -101,7 +101,12 @@ jest.mock('../../src/utils/tokenUtils', () => ({
 }));
 
 jest.mock('../../src/services/recaptcha', () => ({ verifyRecaptcha: () => Promise.resolve(true) }));
-jest.mock('../../src/middleware/sessionTimeout', () => ({ endSession: jest.fn() }));
+// Mock sessionTimeout's isSessionExpired so each test controls the return.
+// Default: not expired (so existing tests keep passing without setup).
+jest.mock('../../src/middleware/sessionTimeout', () => ({
+  endSession: jest.fn(),
+  isSessionExpired: jest.fn(() => Promise.resolve(false)),
+}));
 jest.mock('../../src/utils/logger', () => ({
   info: jest.fn(),
   warn: jest.fn(),
@@ -299,4 +304,92 @@ describe('GET /auth/session — symmetry with protected middleware', () => {
     expect(res.status).toBe(401);
     expect(res.body.valid).toBe(false);
   });
+
+  // Session-timeout symmetry — issue #350 recurrence on v3.39.1-beta.0.
+  // sessionTimeoutMiddleware (mounted on /api/admin) rejects idle/old-iat
+  // tokens with 401 SESSION_TIMEOUT, but /auth/session previously didn't.
+  // The new isSessionExpired helper closes that asymmetry.
+  describe('session-timeout symmetry', () => {
+    const { isSessionExpired } = require('../../src/middleware/sessionTimeout');
+
+    beforeEach(() => {
+      isSessionExpired.mockReset();
+      // Default to "active session" so the other admin checks above also
+      // pass when this branch runs.
+      isSessionExpired.mockResolvedValue(false);
+    });
+
+    it('returns valid:false when isSessionExpired reports the token has timed out', async () => {
+      fakeDb.adminUsers.push({
+        id: 1,
+        username: 'admin',
+        is_active: true,
+        password_changed_at: null,
+      });
+      isSessionExpired.mockResolvedValue(true);
+      const token = signAdminToken({ id: 1 });
+
+      const res = await request(makeApp())
+        .get('/auth/session')
+        .set('Authorization', `Bearer ${token}`);
+      expect(res.status).toBe(200);
+      expect(res.body.valid).toBe(false);
+      expect(res.body.error).toBe('Session expired');
+    });
+
+    it('returns valid:true for an active admin token (helper says not expired)', async () => {
+      fakeDb.adminUsers.push({
+        id: 1,
+        username: 'admin',
+        is_active: true,
+        password_changed_at: null,
+      });
+      isSessionExpired.mockResolvedValue(false);
+      const token = signAdminToken({ id: 1 });
+
+      const res = await request(makeApp())
+        .get('/auth/session')
+        .set('Authorization', `Bearer ${token}`);
+      expect(res.status).toBe(200);
+      expect(res.body.valid).toBe(true);
+      expect(isSessionExpired).toHaveBeenCalledTimes(1);
+    });
+
+    it('does not call isSessionExpired for gallery tokens', async () => {
+      fakeDb.events.push({
+        id: 100,
+        slug: 'wedding',
+        is_active: true,
+        is_archived: false,
+        expires_at: new Date(Date.now() + 86400_000),
+      });
+      const token = signGalleryToken();
+
+      const res = await request(makeApp())
+        .get('/auth/session?slug=wedding')
+        .set('Authorization', `Bearer ${token}`);
+      expect(res.status).toBe(200);
+      expect(res.body.valid).toBe(true);
+      expect(isSessionExpired).not.toHaveBeenCalled();
+    });
+
+    it('falls through (treats as valid) if the helper itself throws', async () => {
+      // Defensive: the require() in auth.js is wrapped in try/catch so a
+      // missing/broken helper doesn't fail-closed during early bootstrap.
+      fakeDb.adminUsers.push({
+        id: 1,
+        username: 'admin',
+        is_active: true,
+        password_changed_at: null,
+      });
+      isSessionExpired.mockRejectedValue(new Error('boom'));
+      const token = signAdminToken({ id: 1 });
+
+      const res = await request(makeApp())
+        .get('/auth/session')
+        .set('Authorization', `Bearer ${token}`);
+      expect(res.status).toBe(200);
+      expect(res.body.valid).toBe(true);
+    });
+  });
 });