How to add a new account in Mac OS if the system has lost them and does not allow adding new ones?

Question

macOS

One fine day, I went to Mail and realized that the system had lost all accounts.
The Account tab in System Preferences->Internet Accounts is also empty.
The Library directory is filled with data.
Ok, I'm trying to add a new account again - I see the Gmail authorization screen, I fill in all the fields, it shows a window asking what to sync-> I click Done and nothing happens.

Answer 1

apple.ru section "Support"

Answer 2

I used apple.com). Support is silent, and users offer to rearrange the system from scratch).
Well, how would this be a universal solution, of course, only this is how the roof flows, let's demolish the house and build a new one))