fix: seed admin user on startup and run sync as background task

- Seed/update admin user from ADMIN_USERNAME/ADMIN_PASSWORD settings on
  startup (admin_users table was empty, login was impossible)
- POST /api/admin/sync now returns immediately and runs the equipment
  sync via BackgroundTasks (full sync took minutes and hit nginx 504)
- run_sync accepts optional sync_log_id to reuse a pre-created log entry
- Adapt admin router test to background sync behavior

backend/app/main.py

@@ -9,6 +9,9 @@ from app.config import get_settings
 from app.database import engine, init_db, async_session
 from app.cache import cache
 from app.routers import equipment, health, admin, rental_requests, contact
+from app.models.admin_user import AdminUser
+from app.auth import get_password_hash
+from sqlalchemy import select
 from app.services.sync_service import SyncService
 from app.services.email_service import EmailService
 from app.mcp_server import get_mcp_app, mcp_session_manager
@@ -36,10 +39,29 @@ async def run_email_retry() -> None:
         logger.info("Email retry complete: %d emails sent", sent)
 
 
+async def seed_admin_user() -> None:
+    """Ensure the admin user from settings exists (create or update password)."""
+    async with async_session() as db:
+        result = await db.execute(
+            select(AdminUser).where(AdminUser.username == settings.admin_username)
+        )
+        user = result.scalar_one_or_none()
+        if not user:
+            db.add(AdminUser(
+                username=settings.admin_username,
+                password_hash=get_password_hash(settings.admin_password),
+            ))
+            logger.info("Seeded admin user %s", settings.admin_username)
+        else:
+            user.password_hash = get_password_hash(settings.admin_password)
+        await db.commit()
+
+
 @asynccontextmanager
 async def lifespan(app: FastAPI):
-    """Application lifespan: init DB, start scheduler, connect cache."""
+    """Application lifespan: init DB, seed admin, start scheduler, connect cache."""
     await init_db()
+    await seed_admin_user()
     await cache.connect()
 
     _mcp_cm = mcp_session_manager.run()