Clipboard copy broken while Copilot CLI is running (Windows)

## Bug Report

### Summary
While the GitHub Copilot CLI app is running, clipboard copy stops working entirely in that process. Selecting text and using right-click copy or Ctrl+C shows a 'copied to clipboard' confirmation, but nothing is actually written to the Windows clipboard — paste returns the previous clipboard content instead.

Clipboard functionality restores immediately upon exiting the CLI with \/exit\.

### Steps to Reproduce
1. Launch GitHub Copilot CLI on Windows
2. Select any text in the session output
3. Right-click → Copy (or Ctrl+C) — shows 'copied to clipboard'
4. Switch to any other app and paste
5. Previous clipboard content is pasted instead of the selected text

Also reproducible via:
\\\powershell
echo 'test' | clip
\\\
Run inside the CLI process — \Get-Clipboard\ reads it back fine within the same process, but the clipboard is not accessible from other applications.

### Expected Behavior
Selected text is copied to the Windows system clipboard and can be pasted in other apps.

### Actual Behavior
'Copied to clipboard' confirmation displays but clipboard is not updated. Previous clipboard content persists.

### Environment
- OS: Windows
- Copilot CLI version: 1.0.66
- RDP (Windows App) was connected at time of discovery but issue persists after disconnecting

### Workaround
Exit the CLI with \/exit\ — clipboard works again immediately in PowerShell.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

No file, test, or entry point is named. First reproduce the failure on Windows by running the CLI and the provided PowerShell clipboard command, then trace how the CLI interacts with the system clipboard. Done means copied CLI text is available to other applications while the CLI remains running, without regressing the documented workaround.

Written by the indexing model from the issue text.