fix(sign-in): detect register mode from URL path, not just query param

Newer Logto versions redirect to /register?app_id=... instead of
/sign-in?first_screen=register. Check the pathname in addition to
the query param so the registration form shows correctly.

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

ui/sign-in/src/SignInPage.tsx

@@ -54,7 +54,9 @@ function pickRandom(arr: string[]) {
 
 function getInitialMode(): Mode {
   const params = new URLSearchParams(window.location.search);
-  return params.get('first_screen') === 'register' ? 'register' : 'signIn';
+  if (params.get('first_screen') === 'register') return 'register';
+  if (window.location.pathname.endsWith('/register')) return 'register';
+  return 'signIn';
 }
 
 export function SignInPage() {