[BUG] Terminal setup only install Claude Code for VSCode in Default profile

Environment

• Platform (select one):
• [x] Anthropic API
• [ ] AWS Bedrock
• [ ] Google Vertex AI
• [ ] Other: <!-- specify -->
• Claude CLI version: 1.0.51
• Operating System: Windows 10
• Terminal: VS Code Terminal

Bug Description

When use Claude Code in Terminal in VS Code, the Terminal Setup only install Claude Code for VSCode in Default profile.

Steps to Reproduce

1. Open VS Code and switch to another VS Code profile.
2. Open Terminal > New Terminal
3. Enter claude in PowerShell
4. Follow the terminal setup process.

<img width="872" height="697" alt="Image" src="https://github.com/user-attachments/assets/71a94b3f-a25d-40af-8c0f-adf385a446a5" />

Expected Behavior

I expected Claude Code to be able to detect the current VS Code profile in use and install Claude Code for VSCode to that profile.

Actual Behavior

Claude Code can only install Claude Code for VSCode to Default profile in VS Code by default.

Additional Context

N/A