Google announced this morning on Twitter that its testing tools can now recognize your Web Story and label it as such. Google said “starting today, our testing tools will recognize if your AMP document is a Web Story. In our testing tools and Performance report we’ll use the term Web Story to identify this format.”
It also shows you two different previews of how it may display in the results:
I do not have access to his performance report but Brodie Clark shared a screen shot on Twitter of his showing Web Story and not AMP Story:
Forum discussion at Twitter.