feat(HAI-003): clear transient task fields when moving to done

- Clear status and worktree in moveTask when target column is done
- Clear transient status in completeTask before moving task to done
- Ensures done tasks don't retain stale status or worktree references

packages/core/src/store.ts

@@ -155,6 +155,12 @@ export class TaskStore extends EventEmitter<TaskStoreEvents> {
     task.column = toColumn;
     task.updatedAt = new Date().toISOString();
 
+    // Clear transient fields when moving to done (matches moveToDone behavior)
+    if (toColumn === "done") {
+      task.status = undefined;
+      task.worktree = undefined;
+    }
+
     const taskJsonPath = join(dir, "task.json");
     this.suppressWatcher(taskJsonPath);
     await writeFile(taskJsonPath, JSON.stringify(task, null, 2));

packages/engine/src/merger.ts

@@ -224,6 +224,8 @@ async function completeTask(
   taskId: string,
   result: MergeResult,
 ): Promise<void> {
+  // Clear transient status before moving to done
+  await store.updateTask(taskId, { status: null });
   // Use moveTask for proper event emission
   const task = await store.moveTask(taskId, "done");
   result.task = task;