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/update_media_item.md

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+# Update Media Item
+
+Update media item metadata (Admin only).
+
+**Endpoint**: `PUT /api/media-items/{media_id}`
+**Auth**: Required (Admin only)
+**Content-Type**: `application/json`
+
+## Path Parameters
+
+| Parameter | Type | Required | Description |
+|-----------|------|-----------|-------------|
+| media_id | string | Yes | Media item UUID |
+
+## Request Body
+
+| Field | Type | Required | Description |
+|--------|------|-----------|-------------|
+| title | string | No | Updated title |
+| author | string | No | Updated author |
+| description | string | No | Updated description |
+| series | string | No | Series name |
+| series_number | integer | No | Number in series |
+
+### Example Request
+
+```json
+{
+  "title": "Updated Title",
+  "author": "Updated Author",
+  "description": "Updated description",
+  "series": "Series",
+  "series_number": 2
+}
+```
+
+## Response (200 OK)
+
+```json
+{
+  "id": "uuid",
+  "title": "Updated Title",
+  "author": "Updated Author",
+  "description": "Updated description",
+  "series": "Series",
+  "series_number": 2,
+  "updated_at": "2026-01-31T10:00:00Z"
+}
+```
+
+## Error Responses
+
+| Code | Description |
+|------|-------------|
+| 400 | Invalid input data |
+| 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 -->