docs: add library and media items API endpoints

Phase 2 part 3: Split library and media item endpoints
- Libraries: get_visible_libraries, get_library, create_library, add_library_folder, set_library_visibility
- Media Items: list_media_items, get_media_item, search_media_items, filter_sort_media_items, update_media_item, delete_media_item
- Complete request/response examples for all endpoints

docs/api/media-items/delete_media_item.md

@@ -0,0 +1,41 @@
+# Delete Media Item
+
+Delete a media item from the library (Admin only).
+
+**Endpoint**: `DELETE /api/media-items/{media_id}`
+**Auth**: Required (Admin only)
+
+## Path Parameters
+
+| Parameter | Type | Required | Description |
+|-----------|------|-----------|-------------|
+| media_id | string | Yes | Media item UUID |
+
+## Request Headers
+
+| Header | Type | Required | Description |
+|--------|------|-----------|-------------|
+| Authorization | string | Yes | Bearer token |
+
+### Example Request
+
+```http
+DELETE /api/media-items/uuid-here
+Authorization: Bearer eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9...
+```
+
+## Response (204 No Content)
+
+Media item deleted successfully.
+
+## Error Responses
+
+| Code | Description |
+|------|-------------|
+| 401 | Invalid or expired token |
+| 403 | User is not an admin |
+| 404 | Media item not found |
+
+## Try It Out
+
+<!-- API Explorer will be inserted here in Phase 3 -->