[FEATURE] Expose active team name in statusline JSON payload

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

When using Agent Teams (TeamCreate, Agent with team_name), there's no way to see which team is currently active in the session. During multi-agent workflows with multiple terminal sessions, it's easy to lose track of which team context you're operating in. The statusline JSON payload currently exposes model info, cost, context usage, and agent name — but nothing about the team.

Proposed Solution

Add team.name (and optionally team.description) to the statusline JSON payload:

{
  "team": {
    "name": "my-project",
    "description": "Working on feature X"
  }
}

Alternatively (or additionally), a built-in command like /team could display the active team info inline.

Alternative Solutions

• Manually reading ~/.claude/teams/{team-name}/config.json, but this requires knowing the team name upfront
• Scanning the ~/.claude/teams/ directory with a custom statusline script, but this is fragile and doesn't know which team the current session belongs to

Priority

Medium - Would be very helpful

Feature Category

Interactive mode (TUI)

Use Case Example

1. I create a team with TeamCreate to coordinate frontend and backend agents
2. I have multiple terminal sessions open — some with teams, some without
3. I glance at my statusline/tmux pane and can't tell which session has which team active
4. With this feature, the statusline would show the team name, letting me instantly identify team context across sessions

Additional Context

Related issues showing community interest in agent/team observability:

• #10052 (Expose current agent info — closed as not planned, but had duplicates #12628, #14306, #15778, #20588)
• #28552 (Agent team termination bug)