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

biome.json

@@ -0,0 +1,59 @@
+{
+    "$schema": "https://biomejs.dev/schemas/2.3.8/schema.json",
+    "vcs": {
+        "enabled": true,
+        "clientKind": "git",
+        "useIgnoreFile": true
+    },
+    "files": {
+        "ignoreUnknown": false
+    },
+    "formatter": {
+        "enabled": true,
+        "indentStyle": "space",
+        "indentWidth": 4
+    },
+    "linter": {
+        "enabled": true,
+        "rules": {
+            "recommended": true,
+            "complexity": {
+                "noImportantStyles": "off"
+            }
+        }
+    },
+    "javascript": {
+        "formatter": {
+            "quoteStyle": "double",
+            "semicolons": "asNeeded"
+        }
+    },
+    "css": {
+        "parser": {
+            "cssModules": true,
+            "tailwindDirectives": true
+        }
+    },
+    "assist": {
+        "enabled": true,
+        "actions": {
+            "source": {
+                "organizeImports": "on"
+            }
+        }
+    },
+    "overrides": [
+        {
+            "includes": ["components/ui/**"],
+            "formatter": {
+                "enabled": false
+            },
+            "linter": {
+                "enabled": false
+            },
+            "assist": {
+                "enabled": false
+            }
+        }
+    ]
+}