VS Code extension: resuming a session doesn't connect to the running CLI session

Description

When opening an active CLI session from the VS Code extension's "past conversations" dropdown, the extension displays the session history but does not properly connect to the running session. Messages entered in the extension do not appear in the CLI, suggesting the extension is either forking the session or opening it in a read-only/disconnected state.

Steps to reproduce

1. Start a Claude Code session in the terminal CLI
2. Have an active conversation going
3. Open the Claude Code VS Code extension (tested in Cursor, a VS Code fork)
4. Find and open the same session from "past conversations"
5. Send a message in the extension
6. Observe that the message does not appear in the CLI session

Expected behavior

Resuming a running session from the extension should fully connect to it — messages sent from either surface (CLI or extension) should appear in both, as a shared session.

Actual behavior

The extension appears to display the session transcript but operates disconnected from the running CLI session. Input in the extension does not reach the CLI.

Environment

• Claude Code CLI (terminal session)
• Claude Code VS Code extension running in Cursor
• macOS