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/AuthPage.jsx

@@ -1,19 +1,16 @@
+import { useState } from 'react';
 import { useApp } from '../context/AppContext.js';
 import { loginUser, registerUser, verifyMfaLogin, logoutUser } from '../syncService.js';
-import { switchStorageUser } from '../utils/bibleUtils.jsx';
 
 export default function AuthPage() {
-  const {
-    authMode, setAuthMode,
-    authForm, setAuthForm,
-    authError, setAuthError,
-    authBusy, setAuthBusy,
-    authMfaPending, setAuthMfaPending,
-    authMfaCode, setAuthMfaCode,
-    authMfaUseBackup, setAuthMfaUseBackup,
-    setAuthUser,
-    setProjectIndex,
-  } = useApp();
+  const { signIn } = useApp();
+  const [authMode, setAuthMode] = useState('login'); // 'login' | 'register'
+  const [authForm, setAuthForm] = useState({ email: '', password: '' });
+  const [authError, setAuthError] = useState('');
+  const [authBusy, setAuthBusy] = useState(false);
+  const [authMfaPending, setAuthMfaPending] = useState(false); // password ok, waiting on TOTP/backup code
+  const [authMfaCode, setAuthMfaCode] = useState('');
+  const [authMfaUseBackup, setAuthMfaUseBackup] = useState(false);
 
   const submitAuth = async (e) => {
     e.preventDefault();
@@ -30,8 +27,7 @@ export default function AuthPage() {
       setAuthMfaPending(true);
       return;
     }
-    setAuthUser(result.data);
-    setProjectIndex(switchStorageUser(result.data.id));
+    signIn(result.data);
   };
 
   const submitMfa = async (e) => {
@@ -48,8 +44,7 @@ export default function AuthPage() {
     }
     setAuthMfaPending(false);
     setAuthMfaCode('');
-    setAuthUser(result.data);
-    setProjectIndex(switchStorageUser(result.data.id));
+    signIn(result.data);
   };
 
   if (authMfaPending) {