feat: add message input with send button and keyboard shortcuts

- MessageInput component with textarea, send button, Enter-to-send
- Shift+Enter for newline, auto-resize textarea
- Disabled state while streaming, auto-focus after send
- Integrated into /chat page with user message handling

Closes #6

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

src/routes/chat/+page.svelte

@@ -1,8 +1,20 @@
 <script lang="ts">
 	import type { ChatMessage } from '$lib/types';
 	import MessageList from '$lib/components/MessageList.svelte';
+	import MessageInput from '$lib/components/MessageInput.svelte';
 
 	let messages: ChatMessage[] = $state([]);
+	let isStreaming = $state(false);
+
+	function handleSend(content: string) {
+		const userMessage: ChatMessage = {
+			id: crypto.randomUUID(),
+			role: 'user',
+			content,
+			timestamp: new Date()
+		};
+		messages.push(userMessage);
+	}
 </script>
 
 <div class="flex h-screen flex-col">
@@ -11,4 +23,5 @@
 	</header>
 
 	<MessageList {messages} />
+	<MessageInput onSend={handleSend} disabled={isStreaming} />
 </div>