Rewrite Quickstart guide with type-checked code examples

.prettierignore

@@ -2,5 +2,6 @@ examples/basic-host/**/*.ts
 examples/basic-host/**/*.tsx
 examples/basic-server-*/**/*.ts
 examples/basic-server-*/**/*.tsx
+examples/quickstart/**/*.ts
 **/vendor/**
 SKILL.md

AGENTS.md

@@ -80,7 +80,7 @@ View (App) <--PostMessageTransport--> Host (AppBridge) <--MCP Client--> MCP Serv
 
 ## Documentation
 
-JSDoc `@example` tags should pull type-checked code from companion `.examples.ts` files (e.g., `app.ts` → `app.examples.ts`). Use ` ```ts source="./file.examples.ts#regionName" ` fences referencing `//#region regionName` blocks, then run `npm run sync:snippets`. Region names follow `exportedName_variant` or `ClassName_methodName_variant` pattern (e.g., `useApp_basicUsage`, `App_hostCapabilities_checkAfterConnection`).
+JSDoc `@example` tags should pull type-checked code from companion `.examples.ts` files (e.g., `app.ts` → `app.examples.ts`). Use ` ```ts source="./file.examples.ts#regionName" ` fences referencing `//#region regionName` blocks; region names follow `exportedName_variant` or `ClassName_methodName_variant` pattern (e.g., `useApp_basicUsage`, `App_hostCapabilities_checkAfterConnection`). For whole-file inclusion (any file type), omit the `#regionName`. Run `npm run sync:snippets` to sync.
 
 Standalone docs in `docs/` (listed in `typedoc.config.mjs` `projectDocuments`) can also have type-checked companion `.ts`/`.tsx` files using the same pattern.