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

.eslintrc.json

@@ -1,6 +1,3 @@
 {
-  "extends": [
-    "next/core-web-vitals",
-    "next/typescript"
-  ]
+    "extends": ["next/core-web-vitals", "next/typescript"]
 }