I don't know how they determine what options to offer, but using my phone was the only one given, despite entering a correct password. The only other option, which I either found from the "Learn more" link or after exhausting the "login with your phone" attempts, was to create a support ticket for my G-suite account which, in this case, would have been slower than returning to home a few hours later where I had left my phone.
That seems to redirect me to the same page linked earlier in this thread (https://myaccount.google.com/security). Taking a look in my admin console, it looks like "Allow users to turn on 2-step verification" is unchecked, so presumably 2-step verification is not enabled for this account. That's exactly what I want, but it seems Google is failing to abide when they think I'm a "hacker". Other people have had the same frustrations[0][1] but there is apparently no way to stop Google requiring additional verification at their whim. Ultimately that means Google controls when I can and can't login to my account, so it ceases to be a usable product for me.
