I don't know who is initiating the prompt and if the company could have done something to prevent this behavior (it may be an unavoidable "feature" of the Google client plug-in). Yet I am pretty confident they knew about this beforehand since the original "Upcoming changes to sign-up flow on the Stack Exchange network" announcement stated that:
We’ll be removing the top banner currently shown to unregistered users on all sites. Instead, we will show a quick sign-up option as a smaller modal near the upper-right corner of the page, that allows users to sign-up using a Google account with a single click (assuming they’re logged in to that account on that browser). This is usually referred to as “Google one-tap.”
Anyway, I will leave further analysis to other users. Here, I just want to point out that as a (hopefully temporary) solution, you can use Adblock or UBlock Origin to stop the domain from loading on the network (this obviously assumes that you are using a Stack Exchange managed account, not a Google one... but I also suspect that if you where using a Google account, the prompt would just try to authenticate you silently)
https://accounts.google.com/$domain=stackexchange.com