Domain not routing mail or logins correctly after tenant transfer

Google is notoriously slow with updating their MX routing. Are you getting any email from external senders at all?

Also check that your device is not still connected/registered/enrolled to your old tenant. Sounds like SSO is kicking in when trying to login to the apps. Try it on a fresh image and/or with a PC enrolled into the new tenant. I'd also suggest that you log a ticket with Microsoft.