Prerequisites:

• Is the functionality available in the GitHub UI? If so, please provide a link to information about the feature.

  Yes. It's available at the github.com/<user/group>/<projectname>/settings/key_links URL

• Is the functionality available through the GitHub API? If the functionality is available, please provide links to the API documentation (https://developer.github.com/v3/) as well as the Octokit documentation (https://octokit.github.io/).

  Yes. API support was [finally] unveiled on 2021-08-02 with this announcement

New Feature

I'm not filing this ticket with any defined schema in-mind that I feel strongly about, but I would at least propose some sort of functionaly like:

references:
  'ASDF-': 'https://jira.company.com/browse/ASDF-<num>'
  'BOLIGRAFO-': 'https://jira.company.com/browse/BOLIGRAFO-<num>'

Where the probot/settings application would be able to manage the Autolink References in a project.