Agent Teams: TaskUpdate status not synced between team and session task lists

Bug Description

When using Agent Teams with a session-level task list, TaskUpdate(status: "completed") calls made while a team is active return success but do not persist to the session task list after TeamDelete.

Steps to Reproduce

1. Create tasks using TaskCreate (session-level task list)
2. Create an Agent Team with TeamCreate
3. Spawn teammates and complete work
4. Call TaskUpdate(taskId: "2", status: "completed") — returns "Updated task #2 status" (success)
5. Call TeamDelete to clean up the team
6. Call TaskList — tasks still show as in_progress instead of completed

Expected Behavior

Tasks updated via TaskUpdate during an active Agent Team session should retain their status after TeamDelete.

Actual Behavior

Tasks revert to their pre-team state (in_progress) after TeamDelete. The updates made during the team session are lost.

Possible Cause

Agent Teams use a separate task list directory (~/.claude/tasks/{team-name}/). When TaskUpdate is called during a team session, it may be updating the team-scoped task list rather than the session-scoped task list. When TeamDelete removes the team directory, the updates are lost.

Environment

• Claude Code CLI
• CLAUDE_CODE_EXPERIMENTAL_AGENT_TEAMS=1
• Agent Teams feature (experimental)

Workaround

Re-call TaskUpdate after TeamDelete to manually sync the status.