John Mueller from Google said that using Google's own domain name service, Google Domains, will not help you rank better in Google search or with your SEO. He said in a Reddit thread "no" when asked "Do migrating to "google domains" will improve my SEO in any way?"
Well, most of that statement is true. If you want me to nitpick, it does help you slightly verify your domain name with Google Search Console. So this helps you get into Google Search Console a bit faster and then Google Search Console has a lot of useful SEO tools that help you with your SEO.
But simply using Google Domains does not help you rank better. Google Domains is not a ranking signal in Google.
I wonder where these theories come from?
Forum discussion at Reddit.