Agent Teams: Teammates don't poll inbox — messages never delivered (tmux backend, macOS)

Bug Description

When using agent teams with the tmux backend on macOS, spawned teammates launch correctly in tmux panes with proper --agent-id/--team-name flags, but never read from their inbox files. Messages sent via SendMessage are written to the inbox JSON files but remain "read": false indefinitely. Teammates behave as standalone Claude Code sessions with no team awareness.

Environment

• Claude Code version: 2.1.32
• OS: macOS (Darwin 25.2.0)
• Terminal: tmux (inside tmux session)
• Model: Opus 4.6 (lead), Haiku 4.5 (teammates)
• Setting: CLAUDE_CODE_EXPERIMENTAL_AGENT_TEAMS=1 in settings.json

Steps to Reproduce

1. Start Claude Code inside a tmux session
2. Create a team via Teammate tool (spawnTeam)
3. Spawn teammates via Task tool with team_name and name params
4. Send messages via SendMessage to teammates
5. Observe teammates never receive the messages

What Happens

• Team config created correctly at ~/.claude/teams/{name}/config.json
• Teammates spawn in new tmux panes (backendType: "tmux")
• Processes launch with correct flags: --agent-id alice@hello-team --agent-name alice --team-name hello-team
• Inbox files written at ~/.claude/teams/{name}/inboxes/{name}.json
• Messages sit in inbox with "read": false forever
• When manually asked in the pane, teammate says: "I haven't received any instructions from a team lead. I'm currently working as a standalone agent."

What Should Happen

Teammates should poll their inbox files and process incoming messages from the team lead and other teammates.

Evidence

Inbox file after sending message (never consumed):

[
  {
    "from": "team-lead",
    "text": "Hello world!",
    "summary": "Saying hello world to alice",
    "timestamp": "2026-02-05T18:56:10.615Z",
    "read": false
  }
]

Tmux pane capture of teammate (alice) showing no team awareness:

❯ Have you received any instructions from the team lead?

⏺ No, I haven't received any instructions from a team lead. I'm currently 
  working as a standalone agent in the Vallum project directory without an
  active team context.

Process running with correct flags:

--agent-id alice@hello-team --agent-name alice --team-name hello-team 
--agent-color blue --parent-session-id 808c58e2-... --agent-type general-purpose 
--dangerously-skip-permissions --model haiku

Additional Context

• Shutdown requests via SendMessage also go undelivered (same inbox issue)
• Teammate cleanup fails because it still sees members as "active"
• The tmux panes are created and Claude Code launches, but the team messaging layer doesn't connect