Yahoo account seems to work, although sometimes it seems to "fall asleep": sincronization sometimes seems don't happen and in this 2 days I've got also an error in sincronization (I just saw a red exclamation point next to the last sync time). This morning, just turned on my cell phone, all my mail accounts synced, except for yahoo...
That "red last sync time" mean -- that the app tried, but ran into network / connectivity errors. Could be some other thing not OAUTH (remember that OAUTH2 is just a particular way to log in, nothing else).
I'd say keep an eye on it and see how it behaves, write back if this remains.
Re: push
For push mail, for "Internet Mail" (IMAP) accounts, Aqua Mail uses the industry standard, well documented, widely supported "IDLE" extension.
It is supported / used by: Gmail, AOL, Hotmail, Yandex, GMX, Fastmail, Web.de services and others, and also servers like Dovecot, Courier, Cyrus and others.
Yahoo however chose to not implement it. I believe they have their own mechanism for push mail which they'd worked out with Apple and which is undocumented.