Team agents in tmux panes start in interactive mode instead of autonomous agent mode

Bug Description

When spawning team agents via the Task tool with team_name parameter, Claude Code correctly opens tmux panes and launches new instances with agent flags, but the agents start in interactive mode (showing ❯ prompt) instead of consuming their inbox messages and running autonomously.

Steps to Reproduce

1. Create a team with Teammate tool (spawnTeam)
2. Create tasks with TaskCreate
3. Spawn agents with Task tool using team_name and name parameters
4. Observe the tmux panes

Expected Behavior

Agents should automatically read their inbox messages and start executing their assigned tasks in autonomous mode.

Actual Behavior

• Tmux panes open correctly
• Claude Code instances launch with correct flags (--agent-id, --agent-name, --team-name, --parent-session-id, --agent-type, etc.)
• Agents start in interactive mode showing the ❯ prompt (e.g., ❯ Try "edit page.tsx to...")
• They never transition to autonomous agent mode
• Inbox messages remain read: false
• tmux send-keys can display text in the pane but Claude Code does not process it

Example Command Launched in Tmux Pane

cd /path/to/project && CLAUDECODE=1 /opt/homebrew/Caskroom/claude-code/2.1.32/claude \
  --agent-id agent-backend@tmux-test \
  --agent-name agent-backend \
  --team-name tmux-test \
  --agent-color blue \
  --parent-session-id <session-id> \
  --agent-type general-purpose \
  --dangerously-skip-permissions \
  --model haiku

Observations

• Tested with both general-purpose and Bash agent types — same behavior
• Tested with haiku model
• SendMessage successfully writes to inbox files, but agents don't poll them
• shutdown_request messages are also ignored
• tmux send-keys + Enter displays text in the pane but the input is not processed by Claude Code's interactive prompt

Environment

• Claude Code version: 2.1.32
• Platform: macOS (Darwin 25.2.0, arm64)
• Node.js: v25.2.1
• tmux: installed via Homebrew
• Shell: zsh