Starting with Arborist 1.3 there is a new preference pane to add accounts for GitHub and GitLab. These are used by Arborist to look for open pull requests (GitHub) and merge requests (GitLab).
These accounts let you specify the host – meaning you can have github.com and git.example.com as independent entries, and you can authorize via the terminal (any token received by Arborist is stored securely) or using a personal access token (also stored in the keychain).
Once this is done you can go back to the main window of the app and in the worktree inspector will be a new section for the account and give you details about an open pull or merge request with a link to it – provided one is open.