Agent Teams: 429/529 API errors on Max plan with concurrent teammates

When using Agent Teams with 5 concurrent teammates, teammates frequently hit 429 (rate limit) and 529 (overloaded) API errors during heavy parallel work sessions.

Environment: Max plan ($200/month), Claude Code 2.1.88, claude-opus-4-6 (1M context), 5 teammates in tmux panes.

Reproduction: Start a team session with 5 specialist teammates. Broadcast a research task to all 5 simultaneously. Within 5-10 minutes, teammates begin receiving 429 and 529 errors with automatic retries (up to 10 with backoff).

Observed: 529 overloaded_error with retryInMs ~590ms, retryAttempt 1 of 10. Tasks that should complete in seconds take minutes. Multiple teammates retrying simultaneously may worsen congestion.

Expected: Max plan should support the concurrency Agent Teams enables. 5 teammates = ~5x request rate of a single session.

Suggestions:

1. Request queuing in Agent Teams to avoid bursting above plan limits
2. Teammate-aware rate limiting (lead throttles based on API pressure)
3. Surface 429/529 to the lead as warnings (currently silent retries)
4. Document concurrent request limits per plan tier for Agent Teams usage

Workarounds: Stagger teammate work, sequence research tasks, reduce team size for heavy phases.