Convert setup guard to startup-driven cache and update tests

backend/app/utils/setup_state.py

@@ -0,0 +1,24 @@
+"""Manage the cached setup completion flag stored on application state."""
+
+from __future__ import annotations
+
+from fastapi import FastAPI
+
+
+def is_setup_complete_cached(app: FastAPI) -> bool:
+    """Return the cached setup completion state from application state."""
+    return getattr(app.state, "setup_complete_cached", False)
+
+
+def set_setup_complete_cache(app: FastAPI, completed: bool) -> None:
+    """Set the cached setup completion state on application state."""
+    app.state.setup_complete_cached = completed
+
+
+def invalidate_setup_complete_cache(app: FastAPI) -> None:
+    """Reset the cached setup completion state.
+
+    This helper exists so the cache can be invalidated explicitly if the
+    application state changes during runtime.
+    """
+    app.state.setup_complete_cached = False