브라우저 리소스 정리 및 종료 처리 개선, 진행 상황 저장 기능 추가

src/lib/llm/prompt/google/prompt.py

@@ -29,6 +29,9 @@ Instructions:
     d. Click the "Sign in" or "Next" button.
 7. If login proceeds without interruptions, wait for redirection back to the original site and record the final URL.
 8. Close your browser window after the login is completed.
+9. Login is considered successful if:
+    - You are redirected to a page that indicates successful login (e.g., a welcome page, dashboard, or account page).
+    - If a page such as a sign-up page appears, consider it a successful login and terminate immediately.
 
 Credentials to use for Google login:
 - Email: {os.getenv("GOOGLE_EMAIL", "")}