Rewrite Quickstart guide with type-checked code examples

Rewrites the Quickstart tutorial to provide a more focused, step-by-step
introduction to building MCP Apps. The guide now uses synced code fences
that pull from `examples/quickstart/`, ensuring all code shown in the
documentation is type-checked and tested.

Key improvements:
- Clearer project setup instructions with explicit commands
- Streamlined explanations of the tool + resource registration pattern
- Added screenshot showing the completed app
- E2E test coverage validates the example works end-to-end

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

examples/basic-server-vue/server.ts

@@ -29,7 +29,7 @@ export function createServer(): McpServer {
       title: "Get Time",
       description: "Returns the current server time as an ISO 8601 string.",
       inputSchema: {},
-      _meta: { ui: { resourceUri } },
+      _meta: { ui: { resourceUri } }, // Links this tool to its UI resource
     },
     async (): Promise<CallToolResult> => {
       const time = new Date().toISOString();