The MediaWiki software doesn't know anything about the assessments, so you're not going to find a separate method to work with them in the API.
There is a bot that maintains a database of assessments, and shows them on a website, but I don't think this data is accessible in a machine-readable format.
So, I think the best way would be just to use categories: all featured articles are in the category Featured articles and you can get the list of those articles using the API method categorymembers
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