[BUG] Only one Claude Code instance per VSCode window can have IDE connection

Description

When running multiple Claude Code instances in different terminals within the same VSCode window, only ONE instance can be IDE-connected at a time. Other instances show IDE: Installed VS Code extension instead of IDE: Connected to VS Code extension.

Steps to Reproduce

1. Open VSCode with Claude Code extension installed
2. Open Terminal 1, run claude, check /status → Shows IDE: Connected
3. Open Terminal 2 (different project folder), run claude, check /status → Shows IDE: Installed (not connected)
4. In Terminal 1, run /exit
5. In Terminal 2, run /ide → Now shows IDE: Connected
6. Go back to Terminal 1, run claude, check /status → Shows IDE: Installed (lost connection)

Expected Behavior

Multiple Claude Code instances in different terminals should be able to connect to the IDE simultaneously, as suggested by the documentation stating "Run multiple Claude Code sessions simultaneously".

Actual Behavior

Only one Claude Code instance per VSCode window can maintain an IDE connection. Starting a new instance or reconnecting from another terminal causes the previous instance to lose its IDE connection.

Environment

• Claude Code version: 2.0.74
• OS: Windows 11 (Build 26200.7462)
• VSCode/Cursor version: Latest
• Terminal: PowerShell (integrated)

Impact

This limitation forces users to either:

1. Work with only one IDE-connected Claude Code at a time
2. Open multiple VSCode windows (~800 MB each) to have multiple simultaneous IDE connections

Related Issues

• #14832 - IDE not connected when running from subdirectory
• #13447 - VSCode integrated terminal cannot detect 'code' command