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

.vscode/settings.json

@@ -0,0 +1,23 @@
+{
+    "editor.formatOnSave": true,
+    "editor.defaultFormatter": "biomejs.biome",
+    "editor.codeActionsOnSave": {
+        "source.fixAll.biome": "explicit",
+        "source.organizeImports.biome": "explicit"
+    },
+    "[javascript]": {
+        "editor.defaultFormatter": "biomejs.biome"
+    },
+    "[typescript]": {
+        "editor.defaultFormatter": "biomejs.biome"
+    },
+    "[javascriptreact]": {
+        "editor.defaultFormatter": "biomejs.biome"
+    },
+    "[typescriptreact]": {
+        "editor.defaultFormatter": "biomejs.biome"
+    },
+    "[json]": {
+        "editor.defaultFormatter": "biomejs.biome"
+    }
+}