fix: Resolve git operation error handling and conflict detection issues

libs/git-utils/src/branch.ts

@@ -0,0 +1,23 @@
+/**
+ * Git branch utilities
+ */
+
+import { execGitCommand } from './exec.js';
+
+/**
+ * Get the current branch name for a given worktree path.
+ *
+ * @param worktreePath - Path to the git worktree
+ * @returns Promise resolving to the current branch name (trimmed)
+ * @throws Error if the git command fails
+ *
+ * @example
+ * ```typescript
+ * const branch = await getCurrentBranch('/path/to/worktree');
+ * console.log(branch); // 'main'
+ * ```
+ */
+export async function getCurrentBranch(worktreePath: string): Promise<string> {
+  const branchOutput = await execGitCommand(['rev-parse', '--abbrev-ref', 'HEAD'], worktreePath);
+  return branchOutput.trim();
+}

libs/git-utils/src/index.ts

@@ -23,3 +23,6 @@ export {
 
 // Export conflict utilities
 export { getConflictFiles } from './conflict.js';
+
+// Export branch utilities
+export { getCurrentBranch } from './branch.js';