[FEATURE] Option to PIN or STAR a session on VS Code plugin

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

There is no option to PIN or STAR a session in VS Code plugin of Claude Code. This is really helpful to keep important session on top.

This option is available all web chat based AIs include the website https://claude.ai/

VS Code Screenshot:
<img width="834" height="521" alt="Image" src="https://github.com/user-attachments/assets/0c6942bc-4786-4372-8aff-53c61e2d6dbb" />

Proposed Solution

Add a feature to PIN of STAR a session by giving it as an icon or a menu option with 3 dots.

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

Interactive mode (TUI)

Use Case Example

_No response_

Additional Context

_No response_