Extract auth into hooks/useAuth; move form state into its pages

- useAuth owns authUser/authServerDown, the startup session check, and
  signIn/logout, so every sign-in path runs the same follow-up (switch
  local storage to the account, load reader ink). Previously reader ink
  only loaded on a page refresh, not right after logging in.
- Login/2FA form state now lives in AuthPage, and 2FA setup, password
  change, and podcast name state in SettingsPage (23 fewer context
  values; typing in these forms no longer re-renders all of App).
- Add tests for form sign-in, 2FA, session restore + logout, and the
  Settings podcast-name prefill.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

src/pages/SettingsPage.jsx

@@ -1,3 +1,4 @@
+import { useState } from 'react';
 import { useApp } from '../context/AppContext.js';
 import {
   startMfaSetup,
@@ -12,21 +13,21 @@ export default function SettingsPage() {
     authUser, setAuthUser,
     authStatus,
     goHome,
-    mfaSetup, setMfaSetup,
-    mfaSetupCode, setMfaSetupCode,
-    mfaSetupError, setMfaSetupError,
-    mfaSetupBusy, setMfaSetupBusy,
-    mfaBackupCodes, setMfaBackupCodes,
-    mfaDisablePassword, setMfaDisablePassword,
-    mfaDisableError, setMfaDisableError,
-    podcastNameInput, setPodcastNameInput,
-    podcastNameSaving, setPodcastNameSaving,
-    podcastNameSaved, setPodcastNameSaved,
-    changePasswordForm, setChangePasswordForm,
-    changePasswordBusy, setChangePasswordBusy,
-    changePasswordError, setChangePasswordError,
-    changePasswordSaved, setChangePasswordSaved,
   } = useApp();
+  const [mfaSetup, setMfaSetup] = useState(null); // { secret, qrCodeDataUrl } while setup is in progress
+  const [mfaSetupCode, setMfaSetupCode] = useState('');
+  const [mfaSetupError, setMfaSetupError] = useState('');
+  const [mfaSetupBusy, setMfaSetupBusy] = useState(false);
+  const [mfaBackupCodes, setMfaBackupCodes] = useState(null); // shown once, right after enabling
+  const [mfaDisablePassword, setMfaDisablePassword] = useState('');
+  const [mfaDisableError, setMfaDisableError] = useState('');
+  const [podcastNameInput, setPodcastNameInput] = useState(authUser?.podcastName ?? '');
+  const [podcastNameSaving, setPodcastNameSaving] = useState(false);
+  const [podcastNameSaved, setPodcastNameSaved] = useState(false);
+  const [changePasswordForm, setChangePasswordForm] = useState({ current: '', next: '', confirm: '' });
+  const [changePasswordBusy, setChangePasswordBusy] = useState(false);
+  const [changePasswordError, setChangePasswordError] = useState('');
+  const [changePasswordSaved, setChangePasswordSaved] = useState(false);
 
   const startSetup = async () => {
     setMfaSetupError('');