The answer to my question was found in this document. (What if someone from the Azure team arrives to meet should really be associated with the "Deployment Configuration" section here )
Windows Azure Websites: How Application Strings and Connection Strings Work
In short, you should not use ConfigurationManager to get settings from a click on application settings IF you are using the .NET 4.5 framework.
If you are not using the .NET 4.5 framework, you should use the Environment.GetEnvironmentVariable .
This worked when I converted my existing environment to App Services. I would really like to warn that I was convinced of it.
EDIT: So that was not the whole story,
The other part is what is meant by the βstickyβ and βnon-stickyβ settings in the documentation. I continued to find links to the fact that the settings were not actually placed in your web.config file, but rather they lived in a properties bag in the memory available to your application. I could not find any reference to how I could see what was in this mysterious bag, but the answer is obvious when you know it.
During swap, any settings in your intermediate slot are actually copied to the settings of your production slot, i.e. actually change it in the slots "Application Settings" in the production slots. And all that is in your slot. The app settings locator is whatβs in the memory properties bag.
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