I was in the same predicament. I finally gave up and contacted Apple Support (in Sweden) and a very skilful and helpful guy helped me through the problem. To solve the problem I had to cancel all three mail accounts I have in System settings. Be sure that you have all data about your accounts stored somewhere or printed out so you can reregister again.
After that I started Mail app again and now it launched but of cource with very few data.
Then I registred the account from my internet provider (but leaving the two accounts which were private domains) and all of a sudden the import begun.
Then we tried to reenter one of the other accounts, but failed when using the private domain email adress. We then changed to the ”original” account (used for redirecting incoming and outgoing mails) which is from the same provider as in the first attempt. Now this account also showed up and imported all stuff related, but as the ”original"email account. The same procedure with the last account was successful, and now I’m very glad that everything is up and running.
So there is some some mismatch between Sonoma and my private adresses which I have to figure out with my domain service provider.
Of course there is a lot of things to sort out (layout, delete old stuff, move certain mailes to right folders etc) before all is back to ”normal” again.