fix(core): prevent duplicate startup logo from nested router lifespan events

FastAPI's merged_lifespan mechanism triggers lifespan events for each
nested router layer. Since program_router is included in v1, which is
included in app, the startup handler was being called 3 times.

Added _startup_done flag to ensure Program.startup() only executes once.

Generated with [Claude Code](https://claude.ai/code)
via [Happy](https://happy.engineering)

Co-Authored-By: Claude <noreply@anthropic.com>
Co-Authored-By: Happy <yesreply@happy.engineering>

backend/src/module/core/program.py

@@ -30,6 +30,10 @@ figlet = r"""
 
 
 class Program(RenameThread, RSSThread, OffsetScanThread):
+    def __init__(self):
+        super().__init__()
+        self._startup_done = False
+
     @staticmethod
     def __start_info():
         for line in figlet.splitlines():
@@ -41,6 +45,10 @@ class Program(RenameThread, RSSThread, OffsetScanThread):
         logger.info("Starting AutoBangumi...")
 
     async def startup(self):
+        # Prevent duplicate startup due to nested router lifespan events
+        if self._startup_done:
+            return
+        self._startup_done = True
         self.__start_info()
         if not self.database:
             first_run()