Gmail password recovery stuck in a never ending loop

So,

1. I forgot my Gmail password

2. I followed the recovery process, in theory successfully (code sent to phone + code sent to 2nd e-mail address)

3. Three days later Google sent me an e-mail at my elected recovery e-mail address saying I can now access my e-mail account (note that Google "recovery success" email does not have any "reset your password" kind of link)

4. I go through the login process and I am taken for another spin in the merry go around: Username: here; Password: I don't remember it; hit "forgot password"; start all over; receive the success e-mail from Google; and so on forever and ever into eternity

Has Google lost its marbles?

I should add: I am still logged in into Gmail both on my PC and my Phone. And I am terrified of logging out of there, as I may never get back. Is this the reason why I am stuck in a loop?

I should also add that, despite the fact that typing www.gmail.com in Chrome takes my straight to my account without asking any questions, there are no traces of my password in Chrome.

Finally, I should add that I have the 2-step verification process enabled.

Any idea on how to get out of the groundhog day?

Thanks!
 

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