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

next.config.ts

@@ -1,8 +1,8 @@
-import type { NextConfig } from "next";
+import type { NextConfig } from "next"
 
 const nextConfig: NextConfig = {
-  /* config options here */
-  output: 'standalone',
-};
+    /* config options here */
+    output: "standalone",
+}
 
-export default nextConfig;
+export default nextConfig