Team config silently disappears while agent UI still shows 'Running'

Bug Report

Problem

When using TeamCreate + Agent to spawn team agents in Claude Desktop, the team config file (~/.claude/teams/{team-name}/config.json) can silently disappear during a session (possibly during context compaction or plan mode transitions).

When this happens:

• Claude Desktop UI still shows all agents as "Running" in the Tasks tab
• Actual state: team config is gone, SendMessage to agents fails silently or has no recipient
• The user has no way to know the agents are effectively dead unless they manually check

Impact

• Wasted time: Without manually checking, users could wait hours for agent responses that will never come
• Silent failure: No error, no notification, no visual indicator in the UI
• Data loss risk: Any in-progress work by agents is lost without notice

Steps to Reproduce

1. Create a team with TeamCreate
2. Spawn agents with Agent tool (dev, tester, inspector)
3. Send work to agents via SendMessage
4. During the session, context compaction or plan mode transition occurs
5. Check ~/.claude/teams/{team-name}/ — config.json is gone
6. UI still shows agents as "Running"

Expected Behavior

1. Team config should persist across context compaction and mode transitions
2. If team config is lost, UI should reflect the actual state (show agents as disconnected/dead)
3. An alert/notification should be shown when team state becomes inconsistent
4. Ideally, a heartbeat mechanism to detect and recover from this state

Environment

• Claude Desktop 1.2773.0 (macOS)
• Claude Code 2.1.92
• Using agent teams (TeamCreate, Agent, SendMessage)

Related

• #48897 (agent progress visibility feature request)