GitHub only issues Copilot tokens through copilot_internal/v2/token to its own
Copilot apps, so a custom GITHUB_COPILOT_CLIENT_ID signed users in and then
failed with no Copilot access. With a custom client ID, look up the account at
copilot_internal/user for the seat and Copilot API address and send the user's
GitHub token straight to Copilot. The default client ID keeps the token swap.