Refactor routers to use explicit FastAPI app dependencies

backend/app/routers/setup.py

@@ -8,9 +8,9 @@ return ``409 Conflict``.
 from __future__ import annotations
 
 import structlog
-from fastapi import APIRouter, HTTPException, Request, status
+from fastapi import APIRouter, HTTPException, status
 
-from app.dependencies import DbDep
+from app.dependencies import AppDep, 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
@@ -43,14 +43,14 @@ async def get_setup_status(db: DbDep) -> SetupStatusResponse:
     summary="Run the initial setup wizard",
 )
 async def post_setup(
-    request: Request,
+    app: AppDep,
     body: SetupRequest,
     db: DbDep,
 ) -> SetupResponse:
     """Persist the initial BanGUI configuration.
 
     Args:
-        request: The incoming HTTP request.
+        app: The FastAPI application instance.
         body: Setup request payload validated by Pydantic.
         db: Injected aiosqlite connection.
 
@@ -74,7 +74,7 @@ async def post_setup(
         timezone=body.timezone,
         session_duration_minutes=body.session_duration_minutes,
     )
-    set_setup_complete_cache(request.app, True)
+    set_setup_complete_cache(app, True)
     return SetupResponse()