Story 15: Implement New Session cancellation

- Call cancel_chat before clearing session state
- Prevents tools from executing silently in background
- Prevents streaming from leaking into new session
- Uses same cancellation infrastructure as Story 13
- Clean session start with no side effects

Closes Story 15

src/components/Chat.tsx

@@ -197,11 +197,17 @@ export function Chat({ projectPath, onCloseProject }: ChatProps) {
 		);
 
 		if (confirmed) {
+			// Cancel any in-flight backend requests first
+			try {
+				await invoke("cancel_chat");
+			} catch (e) {
+				console.error("Failed to cancel chat:", e);
+			}
+
+			// Then clear frontend state
 			setMessages([]);
 			setStreamingContent("");
 			setLoading(false);
-			// TODO: Add backend call to cancel in-flight requests and clear context
-			// invoke("cancel_chat").catch(console.error);
 		}
 	};