For reference, I haven't ever used the Google account for anything like Google Duo, Allo, Hangouts, etc. There was an appeal system linked in the message saying "You broke the terms", but when I filled it out, about 24 hrs later I got a response saying "You can't appeal if you broke the terms", which seems inconsistent at best.
I managed to track down a Google support employee and basically told him "Hey, it should be obvious that I'm a real person and not a bot for a phone carrier". His response at first was "The appeal should work, let me know if it doesn't". I told him that it didn't work, and his response was "Well we're not allowed to help you if the automated system says you broke the terms. You must have broken the terms."
Happy for you getting anything out of them other than a brick wall, at least.
EDIT - To pre-empt some questions that may come up: I was using a unique, randomly generated password for my Google account. Plus, you have to be able to login to the account to see the "You broke the terms" message, so the password was definitely not changed.