feat: 강아지 등록 중성화 필수 선택 + AI 추천 중성화 조건 옵션

- 등록 폼: 중성화 여부(완료/안 함) 필수 토글, 미선택 시 등록 불가
- AI 추천: 중성화 찾기 옵션(상관없음/완료/안 함) → 조건 강아지 중에서만 추천

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

src/api/spots.ts

@@ -40,8 +40,11 @@ export const spotsApi = {
   list: () => http.get<Spot[]>('/api/spots'),
   mates: (spotId: number, userId?: number) =>
     http.get<Mate[]>(`/api/spots/${spotId}/mates${userId ? `?userId=${userId}` : ''}`),
-  aiMates: (spotId: number, dogId: number) =>
-    http.get<AiMate[]>(`/api/spots/${spotId}/ai-mates?dogId=${dogId}`),
+  aiMates: (spotId: number, dogId: number, neutered?: boolean) =>
+    http.get<AiMate[]>(
+      `/api/spots/${spotId}/ai-mates?dogId=${dogId}` +
+        (neutered != null ? `&neutered=${neutered}` : ''),
+    ),
   frequentBreeds: (spotId: number) =>
     http.get<{ breeds: string[] }>(`/api/spots/${spotId}/frequent-breeds`),
   reviews: (spotId: number) => http.get<Review[]>(`/api/spots/${spotId}/reviews`),