Oh funny. They started the recovery process then wanted me to add a phone number so they can send a recovery code. In spite of them first sending a recovery code to the email that I do control and me entering it.

I pressed 'try another way' and they told me they don't have enough information to prove the account is mine.

Fuck off Google basically. They could at least be honest and state that a phone number is required, instead of pretending that it's for verification.