Convert setup guard to startup-driven cache and update tests

backend/app/routers/setup.py

@@ -8,11 +8,12 @@ return ``409 Conflict``.
 from __future__ import annotations
 
 import structlog
-from fastapi import APIRouter, HTTPException, status
+from fastapi import APIRouter, HTTPException, Request, status
 
 from app.dependencies import DbDep
 from app.models.setup import SetupRequest, SetupResponse, SetupStatusResponse, SetupTimezoneResponse
 from app.services import setup_service
+from app.utils.setup_state import set_setup_complete_cache
 
 log: structlog.stdlib.BoundLogger = structlog.get_logger()
 
@@ -41,10 +42,15 @@ async def get_setup_status(db: DbDep) -> SetupStatusResponse:
     status_code=status.HTTP_201_CREATED,
     summary="Run the initial setup wizard",
 )
-async def post_setup(body: SetupRequest, db: DbDep) -> SetupResponse:
+async def post_setup(
+    request: Request,
+    body: SetupRequest,
+    db: DbDep,
+) -> SetupResponse:
     """Persist the initial BanGUI configuration.
 
     Args:
+        request: The incoming HTTP request.
         body: Setup request payload validated by Pydantic.
         db: Injected aiosqlite connection.
 
@@ -68,6 +74,7 @@ async def post_setup(body: SetupRequest, db: DbDep) -> SetupResponse:
         timezone=body.timezone,
         session_duration_minutes=body.session_duration_minutes,
     )
+    set_setup_complete_cache(request.app, True)
     return SetupResponse()