C:/Program Files/Git/terminal-setup fails in Windows Terminal (wt.exe) despite being listed as supported

Description

/terminal-setup fails when running inside Windows Terminal (wt.exe), even though Windows Terminal is listed as a supported terminal in the command's own output.

I've tried all windows terminals: cmd, wt, pwsh...

Steps to reproduce

1. Open Windows Terminal (wt.exe)
2. Launch claude
3. Run /terminal-setup

Expected behavior

The setup should succeed, since Windows Terminal is explicitly listed as a supported terminal.

Actual behavior

The command outputs:

Terminal setup cannot be run from windows-terminal.

And then lists "Windows Terminal" as one of the supported terminals:

To set up the shortcut (optional):
1. Exit tmux/screen temporarily
2. Run /terminal-setup directly in one of these terminals:
   • Windows: Windows Terminal
   ...

This is contradictory — it detects the terminal as windows-terminal but then refuses to run, and tells the user to use the same terminal they're already in.

Environment

• OS: Windows 10 Pro 10.0.19045
• Terminal: Windows Terminal (wt.exe)
• Claude Code: CLI (latest)