When we say that we are "Verified by Google", it is because we have been verified by Google as complying with their OAuth policies for Restricted Scopes. You can see the detailed requirement process here: https://support.google.com/cloud/answer/9110914#restricted-s...
Note: I hope that doesn't come off the wrong way, there is literally a rigorous verification process that you must meet to be verified to connect to the Gmail API via OAuth.
To your point about the badge: we believe Google should provide this type of badge to developers that have paid between $15,000 - $75,000 for the third-party security audit to be able to be even considered verified by Google. Unfortunately, all you get is an email and a fat receipt.
So, we made this badge ourselves. I can understand your point of view that this implies more of a relationship with Google. That is totally fair. If you look at our back and forth with their Trust & Security team last year to secure this verification, you might feel like we had a relationship with them too, haha.
We certainly don't want it to be problematic or misleading. We do think it's important for users to realize that our app is indeed verified and safe to connect to.