Updated 20-Feb-2020
Summary
Azure DevOps pipeline build not able to find NuGet package from our private feed under Artifacts.
Finally, I found the problem. I wonder if this is a bug, or just poorly documented....(or maybe I just didn't interpret it correctly).
As per Leo Lui-MSFT's suggestion above (documented by Microsoft), I'd added the permissions to the NuGet feed, and this didn't work. However, I was intrigued by his sentence:
If you've changed your builds to run at project scope
Personally, I hadn't, so I got with our System Administrator and we went through all the possible settings. Eventually, we found it - it wasn't something I had the ability to change.
So in my example above, BLUE and GREEN are the two projects that are trying to use the NuGet package in RED's Artifact feed.
So picking BLUE (or GREEN), in the bottom left hand corner of Azure DevOps you'll see a link "Project Settings". Under "Pipelines > Settings" there are four settings. We had to change the following to be:
Limit job authorization scope to current project = false
Hope that helps!