Background task completion does not trigger notification (v2.19)

Description

When launching a task in the background using run_in_background: true, the completion of the task does not proactively notify the user. The agent completes silently and the user has to manually check the output file to see the result.

Steps to Reproduce

1. In Claude Code v2.19, start a conversation
2. Have the agent launch a background task (using Task tool with run_in_background: true)
3. Wait for the task to complete

Expected Behavior

Upon task completion, the user should receive a visible notification (e.g., terminal notification, sound, or visual indicator) indicating that the background task has finished.

Actual Behavior

The task completes silently. No terminal notification or system notification is triggered. The user is not aware the task has finished unless they manually check.

Environment

• Claude Code version: 2.19
• Platform: macOS (Darwin 25.0.0)