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/vite.config.ts

@@ -0,0 +1,24 @@
+import { defineConfig } from "vite";
+import { viteSingleFile } from "vite-plugin-singlefile";
+
+const INPUT = process.env.INPUT;
+if (!INPUT) {
+  throw new Error("INPUT environment variable is not set");
+}
+
+const isDevelopment = process.env.NODE_ENV === "development";
+
+export default defineConfig({
+  plugins: [viteSingleFile()],
+  build: {
+    sourcemap: isDevelopment ? "inline" : undefined,
+    cssMinify: !isDevelopment,
+    minify: !isDevelopment,
+
+    rollupOptions: {
+      input: INPUT,
+    },
+    outDir: "dist",
+    emptyOutDir: false,
+  },
+});