[BUG] Plan mode name pill persists in status bar after ExitPlanMode

Bug Report

Description

When plan mode is entered, a colored pill/badge appears in the status bar showing the plan name (e.g., pipeline-end-to-end-review). After the plan is approved and ExitPlanMode completes successfully, this pill remains visible in the status bar. It is never dismissed.

Steps to Reproduce

1. Enter plan mode (e.g., via /plan or a skill that triggers it)
2. Observe the plan name pill appears in the status bar (blue background, plan name text)
3. Complete the plan and approve it when ExitPlanMode is called
4. Expected: The plan name pill disappears from the status bar
5. Actual: The plan name pill remains visible indefinitely

Screenshot

The pill pipeline-end-to-end-review remains in the status bar after plan mode was fully exited and edits were made in normal mode:

The status bar shows:

magrathea [main *+] | Opus 4.6 | 70% context remaining
▸▸ bypass permissions on (shift+tab to cycle)

with the plan name pill still visible above the input area.

Environment

• Platform: macOS (Darwin 25.3.0)
• Interface: CLI (terminal)
• Model: Claude Opus 4.6

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