[FEATURE] Vscode extension claude code show status in session view

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

When you have too many sessions at the same time you can't see which one is running and which one is finished.

Proposed Solution

Should be really nice show icon like loading when session is working so you can identify which session still working and which one finish.

For example, something like do copilot:

<img width="202" height="340" alt="Image" src="https://github.com/user-attachments/assets/71b493a7-1ba7-4233-a7ed-6321233ea14c" />

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

Other

Use Case Example

_No response_

Additional Context

_No response_