[BUG] Agent Teams: Suggestion prompt is always based on conversation with team lead.

Preflight Checklist

• [x] I have searched existing issues and this hasn't been reported yet
• [x] This is a single bug report (please file separate reports for different bugs)
• [x] I am using the latest version of Claude Code

What's Wrong?

When using agent teams (non-tmux mode), the prompt suggestion is always based on the conversation with the team lead.

What Should Happen?

Prompt suggestions should be per-agent.

Error Messages/Logs

Steps to Reproduce

1. Create an agent team.
2. Switch to a different teammate.
3. Observe that you still see the prompt for the team lead.

Claude Model

None

Is this a regression?

No, this never worked

Last Working Version

_No response_

Claude Code Version

2.1.34

Platform

Anthropic API

Operating System

macOS

Terminal/Shell

Terminal.app (macOS)

Additional Information

_No response_