feat(polaris): 完善首页背景与搜索入口视觉

使用本地背景和官方 Provider 图标，闭合状态仅展示当前图标。
调整冷蓝磨砂层次，并移除快捷卡片外部阴影以消除底部色带。
补充搜索 Provider 展示行为测试。

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

ts/web/nextjs/polaris/next-env.d.ts

@@ -1,7 +1,7 @@
 /// <reference types="next" />
 /// <reference types="next/image-types/global" />
-import "./.next/types/routes.d.ts";
-import "./.next/types/root-params.d.ts";
+import "./.next/dev/types/routes.d.ts";
+import "./.next/dev/types/root-params.d.ts";
 
 // NOTE: This file should not be edited
 // see https://nextjs.org/docs/app/api-reference/config/typescript for more information.