Add option to silence teammate-activity broadcasts in agent-teams mode

Problem

When running Claude Code with CLAUDE_CODE_EXPERIMENTAL_AGENT_TEAMS=1 and --teammate-mode tmux, every teammate turn surfaces a one-line activity ping in the team-lead's window (e.g. "scout — teammates running"). For users who want to hold side-conversations directly with a teammate (e.g. a private design session in the teammate pane), this ping steadily consumes the team-lead's context window even though no messages are being sent upstream via SendMessage.

Use case

Team-lead acts as project oversight; individual teammates are used for focused design/research chats that shouldn't pollute the lead's context. Today there's no way to hold those chats inside the team without paying a per-turn context tax on the lead.

Proposed solution

A settings key (e.g. teammate.activityBroadcast: false) or CLI flag (e.g. --quiet-teammate-activity) that suppresses the runtime-level teammate-busy ping from being written to the team-lead pane/context. Explicit SendMessage calls would remain unaffected.

Workaround today

Run design sessions as standalone claude invocations outside the team.

Environment

• Claude Code with CLAUDE_CODE_EXPERIMENTAL_AGENT_TEAMS=1
• macOS (Darwin 24.6.0), tmux teammate mode via claude --teammate-mode tmux