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The promotion API endpoint does not use a NuGet API key, it uses a ProGet API key. It is unfortunate that the terminology is similar, but feed endpoints are handled independently from ProGet API endpoints, so creating a ProGet API key will not interfere with normal dev use of the NuGet feed.
You need to create an API Key in the Admin > API Keys section, and that API key will only be used for ProGet API endpoints (i.e. package promotion, package deployment, and the future "feed management" API).