[FEATURE] Persist visibilty of chat in vscode claude extension

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

After closing the chat window once and reopening it, i have the dropdown with past conversations. after selcting one, the conversation is still not visible anymore.

Proposed Solution

Make the past conversation visible.

Alternative Solutions

_No response_

Priority

High - Significant impact on productivity

Feature Category

Other

Use Case Example

_No response_

Additional Context

_No response_