Background agent label persists after agent completes

Description

After a background agent finishes running, the coloured label/tag for that agent remains visible in the Claude Code UI indefinitely. It does not clear automatically when the agent completes.

Steps to reproduce

1. Launch a background agent using the Agent tool with run_in_background: true
2. Wait for the agent to complete (receive the task-notification)
3. Observe that the coloured label (e.g. "polish-admin-users-tab") remains on the right side of the screen

Expected behaviour

The label should be removed (or marked as done) once the background agent finishes.

Actual behaviour

The label persists after the agent has completed. Ctrl+X Ctrl+K (kill background agents) does not remove it either since no agents are actively running.

Workaround

Restarting the Claude Code session clears the label.

Environment

• Platform: macOS (darwin 24.6.0)