refactor(tui): Move examples from README to test directory

- Move chat application example to test/chat-app.ts
- Move multi-component layout example to test/multi-layout.ts
- Update README to reference example files instead of inline code
- Add proper exit handlers (Ctrl+C) to all examples
- Simplify README by reducing inline code examples

packages/tui/test/chat-app.ts

@@ -0,0 +1,80 @@
+#!/usr/bin/env npx tsx
+import { TUI, Container, TextEditor, MarkdownComponent, CombinedAutocompleteProvider } from "../src/index.js";
+
+/**
+ * Chat Application with Autocomplete
+ * 
+ * Demonstrates:
+ * - Slash command system with autocomplete
+ * - Dynamic message history
+ * - Markdown rendering for messages
+ * - Container-based layout
+ */
+
+const ui = new TUI();
+const chatHistory = new Container();
+const editor = new TextEditor();
+
+// Set up autocomplete with slash commands
+const autocompleteProvider = new CombinedAutocompleteProvider([
+	{ name: "clear", description: "Clear chat history" },
+	{ name: "help", description: "Show help information" },
+	{
+		name: "attach",
+		description: "Attach a file",
+		getArgumentCompletions: (prefix) => {
+			// Return file suggestions for attach command
+			return null; // Use default file completion
+		},
+	},
+]);
+
+editor.setAutocompleteProvider(autocompleteProvider);
+
+editor.onSubmit = (text) => {
+	// Handle slash commands
+	if (text.startsWith("/")) {
+		const [command, ...args] = text.slice(1).split(" ");
+		if (command === "clear") {
+			chatHistory.clear();
+			return;
+		}
+		if (command === "help") {
+			const help = new MarkdownComponent(`
+## Available Commands
+- \`/clear\` - Clear chat history
+- \`/help\` - Show this help
+- \`/attach <file>\` - Attach a file
+			`);
+			chatHistory.addChild(help);
+			ui.requestRender();
+			return;
+		}
+	}
+
+	// Regular message
+	const message = new MarkdownComponent(`**You:** ${text}`);
+	chatHistory.addChild(message);
+
+	// Add AI response (simulated)
+	setTimeout(() => {
+		const response = new MarkdownComponent(`**AI:** Response to "${text}"`);
+		chatHistory.addChild(response);
+		ui.requestRender();
+	}, 1000);
+};
+
+// Handle Ctrl+C to exit
+ui.onGlobalKeyPress = (data: string) => {
+	if (data === "\x03") {
+		ui.stop();
+		console.log("\nChat application exited");
+		process.exit(0);
+	}
+	return true;
+};
+
+ui.addChild(chatHistory);
+ui.addChild(editor);
+ui.setFocus(editor);
+ui.start();