feat: show git branch in footer

- Footer now displays active git branch after directory path (e.g., ~/project (main))
- Branch detected by reading .git/HEAD directly (fast, synchronous)
- Cache refreshed after each assistant message to detect branch changes
- Handles normal branches, detached HEAD, and non-git repos

Closes #55

packages/coding-agent/src/tui/tui-renderer.ts

@@ -589,6 +589,9 @@ export class TuiRenderer {
 
 					// Keep the streaming component - it's now the final assistant message
 					this.streamingComponent = null;
+
+					// Invalidate footer cache to refresh git branch (in case agent executed git commands)
+					this.footer.invalidate();
 				}
 				this.ui.requestRender();
 				break;