Feature Request: Visual completion indicator on conversation list

Summary

When running multiple Claude Code conversations in parallel, there's no way to visually identify which conversation has completed its work. Currently only a sound notification is available via Stop hooks.

Problem

• When multiple chats are running simultaneously, the beep sound tells you something finished but not which one
• Users need to check each conversation manually to find the completed one
• This is especially painful when running 3+ parallel conversations

Proposed Solution

Add a visual indicator (badge, icon, or color change) next to conversations in the conversation list when the agent stops working. Similar to how authentication prompts show a visual indicator.

Possible implementations:

• A checkmark or dot badge next to the conversation name
• A color change on the conversation entry (e.g., green highlight)
• A "Completed" status tag

Context

• Platform: Windows 11 / Desktop App
• Currently using Stop hooks for sound notifications, but visual identification of which conversation is needed
• The authentication permission prompt already has a visual indicator pattern that could be reused

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