chore: add Biome for formatting and linting (#116)

- Add Biome as formatter and linter (replaces Prettier)
- Configure Husky + lint-staged for pre-commit hooks
- Add VS Code settings for format on save
- Ignore components/ui/ (shadcn generated code)
- Remove semicolons, use 4-space indent
- Reformat all files to new style

app/robots.ts

@@ -1,12 +1,12 @@
-import { MetadataRoute } from 'next'
+import type { MetadataRoute } from "next"
 
 export default function robots(): MetadataRoute.Robots {
     return {
         rules: {
-            userAgent: '*',
-            allow: '/',
-            disallow: '/api/',
+            userAgent: "*",
+            allow: "/",
+            disallow: "/api/",
         },
-        sitemap: 'https://next-ai-drawio.jiang.jp/sitemap.xml',
+        sitemap: "https://next-ai-drawio.jiang.jp/sitemap.xml",
     }
 }