Azure DevOps: how to trigger a release upon pull request being completed?

The continuous deployment trigger means, if you specify certain types of artifacts in a release pipeline, you can enable continuous deployment. This instructs Azure Pipeline to create new releases automatically when it detects new artifacts are available.

The Pull request trigger means, once a pull request release is configured, anytime a pull request is raised for the protected branch, a release is triggered automatically, deployed to the specified environments.

So these two triggers are different and more detailed information you can refer to here.

And if you still want to deploy your Nuget after a PR completed, I recommend you to create a new build pipeline and enable the Continuous integration for it. Then set this build pipeline as the Release pipeline Artifact. Because when a PR completed, it will create a new commit to the target branch and this new commit will trigger the build pipeline, and the build pipeline will trigger the release pipeline to deploy the Nuget as your expected.

Not sure if anyone's still looking for a solution to this over a year after the fact, but I was so I wrote an Azure Function app to receive pull request close webhooks from DevOps and translate those events into new releases.

You can find it here on my github:

Feel free to fork it to fit whatever your individual needs are.