Incoming mail no longer runs through a connection per mail provider. You point a subdomain of your own domain at us with an MX record, and mail sent there arrives in the shared inbox, on the timeline of the contact who sent it.
Which account a message belongs to is decided by the address the sending server actually asked for, not by the headers. A blind-copied message names its recipient in no header at all, and would otherwise land nowhere.
With this step the Gmail connection is gone. It required an approval process per provider, repeated every year, and Outlook would have started the same process again. An MX record works with any provider and stays yours.