Yikes, Microsoft does like to make our lives difficult... I definitely feel you that having AppD in your normal deployment workflow would be easiest, but unfortunately a re-architecture of our install process is probably not in the cards. It is definitely something we periodically review though—it's possible that as more and more people have end-to-end package-lock deployment workflows we'll opt to take the work on.
But for us in the mean time it means we need to keep hunting for a better process. If global install on the Azure instances isn't possible, and we have to install into the wwwroot, I wonder, could we use a post-deploy script to install the agent? That way you could have a script that basically changes to the wwwroot directory and runs npm install firstname.lastname@example.org. This same script could set the environment variable. (https://github.com/projectkudu/kudu/wiki/Post-Deployment-Action-Hooks)
Another option would be to do this one-off install at build/deploy time in your CI/CD pipeline somewhere, but depending on your environment that may take more effort. In any case, happy to keep working with you to find something that fits your needs!
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