Now, if I understand John Mueller's tweet correctly, I think he is saying that one visible sign that Google thinks you have a purely flat site architecture is when your site does not show Sitelinks for his name.
John Mueller of Google said on Twitter "If your site has a purely flat architecture, it has no architecture. If all pages are equally important (linked from all other pages), none of the pages are important (relative to the rest of your site). One place where that's often visible is sitelinks (no / "irrelevant" ones)."
Here is the tweet:
If your site has a purely flat architecture, it has no architecture. If all pages are equally important (linked from all other pages), none of the pages are important (relative to the rest of your site). One place where that's often visible is sitelinks (no / "irrelevant" ones)
— 🍌 John 🍌 (@JohnMu) April 9, 2020
Here is an example of sitelinks, if you forgot what they were:
The really only way to control your sitelinks is via your internal site navigation - from what I hear. So a flat site architecture would confuse Google to think all your internal pages are equal.
Forum discussion at Twitter.
