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/quickstart/src/mcp-app.ts

@@ -0,0 +1,26 @@
+import { App } from "@modelcontextprotocol/ext-apps";
+
+// Get element references
+const serverTimeEl = document.getElementById("server-time")!;
+const getTimeBtn = document.getElementById("get-time-btn")!;
+
+// Create app instance
+const app = new App({ name: "Get Time App", version: "1.0.0" });
+
+// Handle tool results from the server. Set before `app.connect()` to avoid
+// missing the initial tool result.
+app.ontoolresult = (result) => {
+  const time = result.content?.find((c) => c.type === "text")?.text;
+  serverTimeEl.textContent = time ?? "[ERROR]";
+};
+
+// Wire up button click
+getTimeBtn.addEventListener("click", async () => {
+  // `app.callServerTool()` lets the UI request fresh data from the server
+  const result = await app.callServerTool({ name: "get-time", arguments: {} });
+  const time = result.content?.find((c) => c.type === "text")?.text;
+  serverTimeEl.textContent = time ?? "[ERROR]";
+});
+
+// Connect to host
+app.connect();