Thanks a lot Greg!
In the end I could solve it without Oauth, but through the two-steps verification and the activation of the App password. Everything repeated for each of my Google accounts.
I think Google should have supplied clear, easy instructions on how getting rid of the problem they created.
Not all users are familiar with this kind of settings, it's not something you use everyday... Google should have spread a step-by-step procedure that anyone could follow.
And Microsoft, knowing that all their Outlook users are affected by Google's policy, should simply do the same - to prevent anybody to panic like it happened to me 😞
So I really thank you for helping, I wish you all the best!
Ciao,
Rita