feat(api): search with Meilisearch (M2)

- artists, albums and tracks indexes are rebuilt from PostgreSQL next
  to the live ones and swapped in, so search keeps working; a rebuild
  runs on start, after every scan and when a source is removed
- transliteration fields (Кино ↔ kino) and a retry in the other
  keyboard layout (ghbdtn → привет) reported as corrected_query
- /search/suggest (3 artists, 3 albums, 5 tracks), /search by type
  with cursor pages, /admin/search/reindex; Meilisearch is part of
  /readyz
- found ids are hydrated from the catalog, so a lagging index never
  returns deleted entries

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

api/openapi.yaml

@@ -14,6 +14,7 @@ tags:
   - name: admin
   - name: library
   - name: catalog
+  - name: search
 security:
   - bearerAuth: []
 paths:
@@ -665,6 +666,72 @@ paths:
                 $ref: "#/components/schemas/Track"
         default:
           $ref: "#/components/responses/Problem"
+  /api/v1/search/suggest:
+    get:
+      operationId: searchSuggest
+      tags: [search]
+      summary: Выпадающий список поиска — до 3 исполнителей, 3 альбомов, 5 треков
+      description: |
+        Если по запросу ничего не найдено, сервер повторяет его в другой раскладке клавиатуры
+        («ghbdtn» → «привет») и возвращает исправленный запрос в `corrected_query`.
+      parameters:
+        - name: q
+          in: query
+          required: true
+          schema:
+            type: string
+            maxLength: 200
+      responses:
+        "200":
+          description: Подсказки
+          content:
+            application/json:
+              schema:
+                $ref: "#/components/schemas/SearchResults"
+        default:
+          $ref: "#/components/responses/Problem"
+  /api/v1/search:
+    get:
+      operationId: search
+      tags: [search]
+      summary: Страница поиска
+      description: |
+        `type=all` — по несколько результатов каждого вида без пагинации;
+        конкретный тип — страницы с `next_cursor`.
+      parameters:
+        - name: q
+          in: query
+          required: true
+          schema:
+            type: string
+            maxLength: 200
+        - name: type
+          in: query
+          schema:
+            type: string
+            enum: [all, artists, albums, tracks]
+            default: all
+        - $ref: "#/components/parameters/Limit"
+        - $ref: "#/components/parameters/Cursor"
+      responses:
+        "200":
+          description: Результаты
+          content:
+            application/json:
+              schema:
+                $ref: "#/components/schemas/SearchResults"
+        default:
+          $ref: "#/components/responses/Problem"
+  /api/v1/admin/search/reindex:
+    post:
+      operationId: reindexSearch
+      tags: [search]
+      summary: Пересобрать поисковые индексы (admin)
+      responses:
+        "202":
+          description: Переиндексация запущена
+        default:
+          $ref: "#/components/responses/Problem"
 components:
   parameters:
     SourceId:
@@ -1461,6 +1528,40 @@ components:
           type: array
           items:
             $ref: "#/components/schemas/Track"
+    SearchResults:
+      type: object
+      required: [artists, albums, tracks, totals, corrected_query, next_cursor]
+      properties:
+        artists:
+          type: array
+          items:
+            $ref: "#/components/schemas/ArtistRef"
+        albums:
+          type: array
+          items:
+            $ref: "#/components/schemas/AlbumSummary"
+        tracks:
+          type: array
+          items:
+            $ref: "#/components/schemas/Track"
+        totals:
+          type: object
+          required: [artists, albums, tracks]
+          description: Оценка общего числа совпадений
+          properties:
+            artists:
+              type: integer
+            albums:
+              type: integer
+            tracks:
+              type: integer
+        corrected_query:
+          type: string
+          nullable: true
+          description: Запрос в другой раскладке, если по исходному ничего не нашлось
+        next_cursor:
+          type: string
+          nullable: true
     Session:
       type: object
       required: [id, device_name, client_type, created_at, last_used_at, current]