Fix require_cap TypeError, rewrite /analysis/comparison, add room category sync

- require_cap was a Depends-factory but every call site uses it inline;
  make it an inline checker (fixes 500 on /analysis/hotels, /direct/*)
- /analysis/comparison returned a per-date matrix the frontend never read;
  return per-hotel aggregates (our/their avg, price index) and default to
  all active competitors so the Market Comparison table works without params
- Room categories were never populated (lost in port): add sites_list fetch
  to the Newbook client, categories list/sync/toggle endpoints, and a
  Settings card — without included categories every rates sync exits early

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

backend/services/newbook_rates_client.py

@@ -93,6 +93,39 @@ class NewbookRatesClient:
             "region": self.region
         }
 
+    async def get_room_categories(self) -> List[Dict]:
+        """
+        Fetch room categories by grouping the sites_list endpoint.
+
+        Each site includes site_category_id and site_category_name; categories
+        are derived by grouping sites and counting rooms per category.
+
+        Returns:
+            List of dicts with {category_id, category_name, room_count}
+        """
+        payload = self._get_auth_payload()
+        response = await self.client.post(
+            self._get_url("sites_list"),
+            json=payload,
+            auth=(self.username, self.password)
+        )
+        response.raise_for_status()
+        sites = response.json().get("data") or []
+
+        categories: Dict[str, Dict] = {}
+        for site in sites:
+            cat_id = str(site.get("site_category_id") or "")
+            if not cat_id:
+                continue
+            entry = categories.setdefault(cat_id, {
+                "category_id": cat_id,
+                "category_name": site.get("site_category_name") or f"Category {cat_id}",
+                "room_count": 0,
+            })
+            entry["room_count"] += 1
+
+        return sorted(categories.values(), key=lambda c: c["category_name"])
+
     async def get_category_rates(
         self,
         category_id: str,