Google's John Mueller said that the performance of your Web Stories in Google Search is not related to the overall ranking performance of your site in general in Google Search. He also added a side not that in general, Web Stories are hard to optimize for SEO because Web Stories typically have very little textual content.
John said this in his latest YouTube SEO hangout at the 42:51 mark, where he said "I would not worry that the performance of the Web Stories somehow relates to the ranking of the rest of your content because that's that's definitely not the case."
He then briefly commented about how it is hard to do SEO on these Web Stories, saying "I think with Web Stories themselves doing SEO for them is sometimes tricky because there's very little text on them. So if you're getting impressions for them then you're already doing some some really good work."
Then he went back to how Web Stories do not impact your other pages on your site, in terms of rankings. He said "But in general these are essentially HTML pages they're presented in a slightly different way in the search results and then Discover but it's not going to be that those web stories will negatively affect the rest of your website's ranking."
Here is the video embed:
Just some history on Web Stories, in 2018, Google launched AMP Stories and then they got more visual, with visual stories in 2019. Then in 2020, Google renamed them from AMP Stories to Web Stories.
Forum discussion at YouTube Community.
