feat(web): settings to keep the search open and hide home pickers; collapsible menu sections

- appearance settings get "collapse search" (off keeps the field always open)
  and separate switches for the activity and mood pickers on the home page;
  stored in ui_prefs (search_collapse, home_activities, home_moods)
- Collection and Admin headers in the sidebar fold their items; the state is
  remembered in the browser, a folded Admin shows the review queue badge;
  icon-only and phone layouts always show every item

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

packages/api-client/src/generated/schema.ts

@@ -1514,6 +1514,12 @@ export interface components {
              * @enum {string}
              */
             search_position?: "center" | "left" | "right";
+            /** @description Сворачивать поиск в кнопку с лупой без фокуса (по умолчанию true) */
+            search_collapse?: boolean;
+            /** @description Показывать на главной веба выбор занятия (по умолчанию true) */
+            home_activities?: boolean;
+            /** @description Показывать на главной веба выбор настроения (по умолчанию true) */
+            home_moods?: boolean;
             /** @enum {string} */
             mobile_player?: "cover" | "wave";
             ambient?: boolean;