refactor: 改进调度器启动逻辑并清理日志

- 修改 `key_checker.py` 中的调度器启动逻辑，确保即使实例存在但未运行时也能启动。
- 在 `key_checker.py` 中添加了调度器启动和状态日志。
- 移除了 `application.py` 中数据库断开连接和调度器停止时的冗余关闭日志。

app/core/application.py

@@ -54,7 +54,6 @@ async def _setup_database_and_config(app_settings):
 async def _shutdown_database():
     """Disconnects from the database."""
     await disconnect_from_db()
-    logger.info("Disconnected from database.")
 
 def _start_scheduler():
     """Starts the background scheduler."""
@@ -67,7 +66,6 @@ def _start_scheduler():
 def _stop_scheduler():
     """Stops the background scheduler."""
     stop_scheduler()
-    logger.info("Scheduler stopped.")
 
 async def _perform_update_check(app: FastAPI):
     """Checks for updates and stores the info in app.state."""

app/scheduler/key_checker.py

@@ -90,8 +90,10 @@ scheduler_instance = None
 
 def start_scheduler():
     global scheduler_instance
-    if scheduler_instance is None:
+    if scheduler_instance is None or not scheduler_instance.running:
+        logger.info("Starting scheduler...")
         scheduler_instance = setup_scheduler()
+    logger.info("Scheduler is already running.")
 
 def stop_scheduler():
     global scheduler_instance