fix: hide registration option when sign-in mode is SignIn only

Fetch /api/.well-known/sign-in-exp on mount and check signInMode.
If not SignInAndRegister, hide the "Sign up" link and force sign-in
mode (even if ?first_screen=register was in the URL).

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

ui/sign-in/src/SignInPage.tsx

@@ -61,6 +61,7 @@ function getInitialMode(): Mode {
 
 export function SignInPage() {
   const [mode, setMode] = useState<Mode>(getInitialMode);
+  const [registrationEnabled, setRegistrationEnabled] = useState(true);
   const subtitle = useMemo(
     () => pickRandom(mode === 'signIn' ? SIGN_IN_SUBTITLES : REGISTER_SUBTITLES),
     [mode === 'signIn' ? 'signIn' : 'register'],
@@ -75,6 +76,18 @@ export function SignInPage() {
   const [error, setError] = useState<string | null>(null);
   const [verificationId, setVerificationId] = useState('');
 
+  // Fetch sign-in experience to check if registration is enabled
+  useEffect(() => {
+    fetch('/api/.well-known/sign-in-exp')
+      .then((r) => r.json())
+      .then((data) => {
+        const enabled = data.signInMode === 'SignInAndRegister';
+        setRegistrationEnabled(enabled);
+        if (!enabled && mode !== 'signIn') setMode('signIn');
+      })
+      .catch(() => {});
+  }, []);
+
   // Reset error when switching modes
   useEffect(() => { setError(null); }, [mode]);
 
@@ -211,12 +224,14 @@ export function SignInPage() {
                 Sign in
               </Button>
 
-              <p className={styles.switchText}>
-                Don't have an account?{' '}
-                <button type="button" className={styles.switchLink} onClick={() => switchMode('register')}>
-                  Sign up
-                </button>
-              </p>
+              {registrationEnabled && (
+                <p className={styles.switchText}>
+                  Don't have an account?{' '}
+                  <button type="button" className={styles.switchLink} onClick={() => switchMode('register')}>
+                    Sign up
+                  </button>
+                </p>
+              )}
             </form>
           )}