Google seems to be testing displaying the domain the web story is from, while on the web story, in the footer of the story. Also, Google also shows tips on how to interact with web stories when you first load a web story from Google Search.
Brodie Clark posted about this on Twitter earlier this week, showing both. I personally do not see the domain banner in the footer, but he does, here is his screenshot of that:
I do like that Google is amplifying the domain name of this web story at the bottom of the web story, by also adding the site's favicon and domain name.
Google also shows these interactive instructions when you first access the web story. Here is a GIF of it in action:
I have yet to really do many web stories myself but maybe I should try more...
Forum discussion at Twitter.
