I was directed to this page from https://docs.microsoft.com/en-us/azure/devops/pipelines/artifacts/nuget?view=azure-devops&tabs=yaml#publish-your-packages where I was unable to set up permissions for a build. Turns out that when setting up pipleine publishing to the feed, there are useful options under the ellipsis menu to Allow project-scoped builds and Allow builds and releases. Since the users mentioned in "Package permissions in Azure Pipelines" do not appear in the auto-complete (for my organization, at least), I could not add the permissions I was expecting. These dropdowns not only gave access to the user, but set up the role correctly, automatically! It would be incredibly helpful if these options were mentioned in the documentation rather than just the principle names.
Terms I was searching for, in case anyone else needs to find this issue, included "azure devops pipeline publishVstsFeed permissions".
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Screenshot for completeness:

Note the options are disabled because I have already selected them.
Dude! This TOTALLY needs to be added to the docs! Thank you for finding this.
You just need to add a section at the end of that paragraph that mentions how to set up the permissions for the project-scoped build identity automatically.
Under feeds settings > permissions, you can click on the ellipsis on top to get a menu where you can click on Allow project-scoped builds. The comment by mdekrey has the screenshot for this
@mdekrey Thank you for the great feedback. The updated article will go live shortly.
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Screenshot for completeness:

Note the options are disabled because I have already selected them.