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/hooks/useAuth.js

@@ -0,0 +1,44 @@
+// Who is signed in. Checks the session on startup and exposes signIn/logout so
+// every sign-in path (startup, login form, 2FA) runs the same follow-up work.
+import { useEffect, useRef, useState } from 'react';
+import { getCurrentUser, logoutUser } from '../syncService.js';
+
+// onSignIn(user) runs right after a user becomes signed in (switch local
+// storage to their account, load their data). onSignOut() runs after logout.
+export function useAuth({ onSignIn, onSignOut }) {
+  // authUser: undefined = still checking · null = signed out · object = signed in
+  const [authUser, setAuthUser] = useState(undefined);
+  const [authServerDown, setAuthServerDown] = useState(false);
+
+  // Callbacks come from App and close over its latest state; read them through
+  // a ref so signIn/logout never call a stale copy.
+  const callbacksRef = useRef({ onSignIn, onSignOut });
+  callbacksRef.current = { onSignIn, onSignOut };
+
+  const signIn = (user) => {
+    setAuthUser(user);
+    callbacksRef.current.onSignIn(user);
+  };
+
+  const logout = async () => {
+    await logoutUser();
+    setAuthUser(null);
+    callbacksRef.current.onSignOut();
+  };
+
+  useEffect(() => {
+    getCurrentUser().then((result) => {
+      if (result.ok) {
+        if (result.user) signIn(result.user);
+        else setAuthUser(null);
+      } else {
+        // Genuine network failure (server unreachable) — fall back to local-only mode.
+        setAuthServerDown(true);
+        setAuthUser(null);
+      }
+    });
+    // eslint-disable-next-line react-hooks/exhaustive-deps
+  }, []);
+
+  return { authUser, setAuthUser, authServerDown, signIn, logout };
+}