The GitHub Copilot API now requires a Copilot-Integration-Id header
on all requests. Without it, every API call fails with HTTP 400:
"missing required Copilot-Integration-Id header".
Uses vscode-chat as the integration ID, matching opencode which
shares the same OAuth client ID (Ov23li8tweQw6odWQebz).
Fixes: Copilot provider fails with "missing required Copilot-Integration-Id header" (HTTP 400)
Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>