Add initial Nuxt 4 project setup with essential configurations

- Created .gitignore to exclude build outputs, logs, and environment files.
- Added nuxt.config.ts for project configuration, enabling Tailwind CSS and Pinia modules.
- Initialized package.json with scripts for development and production, and added necessary dependencies.
- Generated pnpm-lock.yaml for dependency management.
- Created README.md with setup instructions and development guidelines.
- Implemented server API examples in server/api/ directory, demonstrating various use cases.
- Added middleware for logging requests and responses.
- Included example Vue components and pages for server API interaction.
- Established basic project structure for Nuxt 4 application development.

.claude/settings.local.json

@@ -0,0 +1,17 @@
+{
+  "permissions": {
+    "allow": [
+      "Bash(npm create nuxt@latest my-app -- --no-install 2>&1)",
+      "Bash(echo \"1\" | npx nuxi@latest init my-app 2>&1 | head -50)",
+      "Bash(npx nuxi@latest init my-app --template minimal 2>&1)",
+      "Bash(printf '\\\\n' | npx nuxi@latest init my-app --template minimal --packageManager pnpm 2>&1)",
+      "Bash(cd /Users/hyeonggilkim/01.Study/nuxt4/my-app && pnpm install 2>&1)",
+      "Bash(pnpm approve-builds 2>&1)",
+      "Bash(printf 'a\\\\n' | pnpm approve-builds 2>&1 || true)",
+      "Bash(npx nuxi module add @nuxtjs/tailwindcss 2>&1)",
+      "Bash(npx nuxi module add @pinia/nuxt 2>&1)",
+      "mcp__nuxt-remote__get-documentation-page",
+      "mcp__ide__getDiagnostics"
+    ]
+  }
+}