InconsistentPublicationsError: Site is published to multiple domains at various times

We are updating and adding content to the Webflow collection in real-time. We are using Zoho Flow (a tool like Zapier). This was working properly till a couple of weeks ago and we were able to update the CNS collection in real-time. But now we are receiving the following error:

InconsistentPublicationsError: The site is published in multiple domains at various times.

Help to solve is highly appreciated

Here is my public share link: LINK
(how to access public share link)

You have to publish your site to all your domains. Then that API call will work again.

I am getting the same issue - however I cannot publish via Designer UI - the * domain is grayed out (and behind in time behind main custom domain) and I cannot publish. Has anyone encounter something like this?