Oh my god. 2-Step verification on your Google Account is actually less secure than not using it at all. I just posted about something similar maybe 3 months ago?[1] > I kid you not. Google's actual official answer to this is... create another account![1][2][3] > Edit: Now that I have your attention: > PSA: Go create "Backup codes" for your Google Account in your 2-Step Verification settings. > [1]: https://support.go…
I have 2FA backup codes! They let me log into my account! But using only backup codes, I cannot remove the lost 2FA. So now I have 8 consumable backup codes and after that I will not be able to access the account. To remove the lost 2FA, I need a fresh 2FA code. No alternatives given.
However, I also think that Google keeps track of a "security rating" for your session; when I don't log in for a while, Google asks me for my password but when I use that same session token on another physical address I also need to authenticate with 2FA.
This may imply that failed login attempts may flag your session as even worse than before. I have no idea if this is actually how it works or if this is purely coincidental, but it may be worth keeping in mind given that you have limited backup codes available to you.
My recommendation would be to first get a Google Takeout backup stored somewhere safe, then see if you can get another 2FA method that you have control over connected to your account.