[BUG] Plan mode name label on input separator persists after plan execution completes (CLI)

Summary

When a plan is accepted and executed via EnterPlanMode/ExitPlanMode in the CLI terminal, a cyan-colored label showing the plan name (e.g., "packing-list-refactor") appears on the right side of the input separator line. After plan execution completes, this label does not clear. The only way to remove it is /clear (which destroys the entire session).

Current behavior

1. Enter plan mode (via EnterPlanMode or Shift+Tab)
2. Write and accept a plan → cyan plan name label appears on the separator line
3. Plan executes and completes successfully
4. Label remains on the separator line indefinitely
5. Only /clear removes it

Expected behavior

The plan name label should clear automatically when plan execution is complete (i.e., all plan steps have been implemented and the plan context is no longer active).

Environment

• Claude Code version: 2.1.79
• Platform: Windows 11 (CLI terminal, not VS Code)
• Model: claude-opus-4-6 (1M context)
• Shell: bash (Git Bash on Windows)

Notes

• The plan name appears to be auto-generated from plan content (session naming feature added in v2.1.77+)
• Related but distinct from VS Code plan display issues (#33525, #32758)
• No hook or setting exists to control this label or dismiss it programmatically