[BUG] Forked sessions not appearing in /resume list and session unexpectedly terminating

Bug Description

Two related issues with forked sessions:

1. Forked sessions don't appear in /resume list: When a session is forked, the forked session does not show up in the /resume command's session list, making it impossible to resume later using session name.

1. Forked session unexpectedly terminates: The forked session terminated unexpectedly without user action.

Steps to Reproduce

1. Start a Claude Code session
2. Fork the session (context compaction triggers fork)
3. Continue working in the forked session
4. Use /resume command - the forked session is not listed
5. The forked session may also terminate unexpectedly

Expected Behavior

• Forked sessions should appear in /resume list with their session name
• Forked sessions should not terminate unexpectedly
• Session IDs (UUIDs) are not human-memorable, so session names should be the primary way to identify and resume sessions

Environment

• Platform: macOS (darwin)
• Claude Code Version: Latest
• Session ID: 8dcebbb9-997c-439e-a7aa-6c5cba617ade
• Session Name: 保護者編集画面の通知設定UI

Additional Context

The session was created via context compaction fork. The user had to use /status command to find the session name since /resume didn't show it.

Related issues (but different problems):

• #22030 - Resume shows only partial conversation history
• #22107 - Session resume logic losing context
• #12235 - Session ID changes when resuming