One can still call the Jenkins API by using Jenkins tokens or use the Jenkins CLI with an SSH key for authentication. However, the GitHub OAuth plugin provides another way to call the Jenkins API by allowing the use of a GitHub Personal Access Token.
However, I cannot make SSH authentication work (by adding SSH keys to the users being created by the extension) nor Jenkins tokens work (by using the tokens from their profiles).
The only authentication option seems to be:
Is the documentation outdated or is it a regression?