Agent Teams: stream each team member's output to cmux panes

Summary

When using Agent Teams with cmux, it would be valuable to have each team member's work automatically displayed in a separate cmux pane, allowing real-time visual monitoring of all agents working in parallel.

Current behavior

• Agent Teams members run as internal processes within Claude Code
• Their work is not visible until they return results
• cmux supports pane splitting and screen reading, but there's no integration between Agent Teams and cmux panes

Desired behavior

When Agent Teams spawns team members, each member's thinking/tool usage/output is streamed to a dedicated cmux pane in real-time. This would allow users to:

1. Visually monitor all team members working simultaneously
2. See each agent's reasoning and progress as it happens
3. Quickly identify if any agent is stuck or going in the wrong direction

Possible implementation

• Detect cmux environment (CMUX_* env vars)
• On TeamCreate/Agent spawn, auto-create a cmux split pane per agent
• Route each agent's output stream to its corresponding pane
• Clean up panes when agents complete

Environment

• Claude Code v2.1.84
• cmux v0.62.2-nightly
• macOS

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