feat(representation): expose doctor representation details and add counts in admin views

docs/api/admin.md

@@ -357,13 +357,18 @@ List all doctors with pagination.
       "degree": "متخصص",
       "gender": "male",
       "doctor_rate": 4.5,
-      "active_doctor_appointment": true
+      "active_doctor_appointment": true,
+      "representation_id": 12,
+      "representation_uuid": "9c1...",
+      "representation_name": "علی محمدی"
     }
   ],
   "meta": { "totalRecords": 92, "totalPages": 5, "currentPage": 1 }
 }
 ```
 
+> `representation_id`/`representation_uuid`/`representation_name` نماینده‌ی مالکِ پزشک‌اند؛ برای پزشکانِ بدون نماینده (مثل ایمپورت‌های IRIMC) هر سه `null`.
+
 ---
 
 ### GET `/api/v1/admin/doctors/stats`
@@ -761,18 +766,57 @@ Paginated representation list. Each item:
   "city": "یزد، تهران",
   "commission_percent": 10.0,
   "wallet_balance": 0,
+  "doctor_count": 14,
+  "appointment_count": 231,
   "is_active": true,
   "created_at": "2026-06-18T..."
 }
 ```
 > `city_id` = اولین شهر (BC)؛ `city` = نام شهرها با «،». `is_global=true` یعنی نماینده سراسری (badge در پنل).
 
+> `doctor_count` = تعداد پزشکانِ `representation_id = r.id`؛ `appointment_count` = تعداد نوبت‌های آن پزشکان. هر دو با کوئری گروهی محاسبه می‌شوند (بدون N+1).
+
 > `mobile_number` falls back to the linked user's mobile when the representation's own `mobile_number` column is empty.
 
 > **Deactivation, not deletion:** the admin panel deactivates a representation via `PATCH /api/v1/representation/{uuid}` with `{ "active": false }` rather than calling `DELETE`.
 
 ---
 
+### GET `/api/v1/admin/representations/{uuid}/doctors`
+
+پزشکان زیرمجموعه‌ی یک نماینده (paginated).
+
+**Permission:** `ROLE_ADMIN`
+
+### Query Parameters
+| Param | Type | Required | Description |
+|-------|------|----------|-------------|
+| `page` | integer | ❌ | Default: 1 |
+| `limit` | integer | ❌ | Default: 15 (max 100) |
+
+### Response `200`
+Paginated. Each item:
+```json
+{
+  "uuid": "...",
+  "id": 45,
+  "name": "دکتر علی احمدی",
+  "gender": "man",
+  "medical_code": "12345",
+  "is_active": true,
+  "owner_status": "claimed",
+  "appointment_count": 17,
+  "created_at": "2026-06-18T..."
+}
+```
+
+### Errors
+| Code | HTTP | Description |
+|------|------|-------------|
+| `ERR_NOT_FOUND_001` | 404 | نماینده یافت نشد |
+
+---
+
 ## Secretary Management
 
 ### GET `/api/v1/admin/secretaries`