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/public/icons/bing.svg

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ts/web/nextjs/polaris/public/icons/github.svg

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ts/web/nextjs/polaris/public/icons/google.svg

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ts/web/nextjs/polaris/public/icons/local.svg

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