Title: Extension update silently deletes conversation history without warning or migration

Preflight Checklist

• [x] I have searched existing issues and this hasn't been reported yet
• [x] This is a single bug report (please file separate reports for different bugs)
• [x] I am using the latest version of Claude Code

What's Wrong?

Body: Auto-update from Claude Code 2.1.34 to 2.1.39 in VSCode silently destroyed all stored conversation history. No warning was shown, no migration was performed, and no backup was created. The user relied on conversation persistence between sessions as their primary development workflow for an embedded systems project (ESP32/PlatformIO). After the update, only the current session exists - all prior conversation files are gone from the .claude/projects/ directory. Conversation history is work product and should be preserved or at minimum backed up during extension updates.

What Should Happen?

all prior conversation files are gone from the .claude/projects/ directory. Conversation history is work product and should be preserved or at minimum backed up during extension updates.

Error Messages/Logs

Steps to Reproduce

I don't know - start a session, then close it then reopen it?

Claude Model

None

Is this a regression?

Yes, this worked in a previous version

Last Working Version

_No response_

Claude Code Version

Claude Code extension version 2.1.34., with 2.1.39 installed (the update that likely caused the history loss). VSCode may be running the older one currently, with the newer one waiting for a reload.

Platform

Anthropic API

Operating System

macOS

Terminal/Shell

Terminal.app (macOS)

Additional Information

_No response_