Agent worktrees created in /tmp cause data loss on reboot

Bug

When Claude Code spawns agents with isolation: "worktree", the git worktree is created in the system temp directory (/private/tmp on macOS) rather than in .claude/worktrees/ inside the project. macOS purges /private/tmp on reboot, which destroys the worktree working directory and any uncommitted changes, leaving a stale git worktree reference.

Reproduction

1. Open Claude Code in a git repository
2. Have Claude spawn an agent with isolation: "worktree" (this happens automatically for background agents working on code)
3. The worktree is created at /private/tmp/<name> instead of <repo>/.claude/worktrees/<name>
4. Reboot the machine
5. The worktree directory and all uncommitted work is gone
6. git worktree list still shows the stale reference pointing to the now-deleted /private/tmp path

Evidence

User-initiated worktrees (via EnterWorktree) correctly go to .claude/worktrees/:

/path/to/repo/.claude/worktrees/agent-a27332e1

But agent-spawned worktrees go to /private/tmp:

/private/tmp/phase4   91a6445bc2fa [username/submission-eligibility]

Impact

• Data loss: uncommitted work in the agent worktree is permanently lost on reboot
• Stale git state: git worktree list shows orphaned entries requiring manual git worktree prune
• Users may not realize work is in a temp directory and won't know to commit before rebooting

Expected behavior

Agent-spawned worktrees should be created in .claude/worktrees/ (consistent with EnterWorktree) or another non-temp location that persists across reboots.

Environment

• Claude Code: 2.1.74
• macOS 26.3.1 (Darwin 25.3.0)
• Model: claude-opus-4-6[1m]