[FEATURE] tabs in vscode sidebar chat

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

I often need to have multiple open sessions with Claude code in VSCode. Now I have to open multiple editor tabs with Claude. But editor tabs are not like sidebar which can be easily toggled to hide/show.

Proposed Solution

It would be a better experience if we could support tabs in the Claude sidebar in VSCode.
Thank you!

Alternative Solutions

_No response_

Priority

High - Significant impact on productivity

Feature Category

Other

Use Case Example

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Additional Context

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