Can't see Jenkins Build status in GitHub

Up until now our Jenkins server polled the repo-status every 10 minutes and triggered a rebuild if changes were detected. To get more safety for our PRs, I wanted to activate the “Merge only when status-checks pass” option for the repository. However I didn’t find a way to show the build-status for our Repository.

I tried following the official guide to set up the build-status integration (this answer is even linked to from the Jenkins GitHub-plugin page). However I face two problems:

  1. The guide mentions to add an option in the Post-Build-actions of the job. However, there aren’t any Post-Build-actions visible for the job in question:
  2. I also work on another project (different GitHub-organization, different Jenkins-instance), where the build-status is correctly reported. After talking to the responsible person, he told me, that this was added automatically for him, when he set up the webhook. This wasn’t working for me. Also, this second Jenkins-instance also doesn’t show any Post-Build actions for the builds, that successfully report the status.

Versions are:

Jenkins: 2.349
GitHub: Enterprise 3.3.7
Jenkins GitHub plugin: 1.34.5

If I can help with any other information, please feel free to ask.