A few years ago, we moved all of our on-prem Exchange 2010 users to Exchange Online using a full hybrid migration. When have no on-prem Exchange servers anymore.
Many of the changes we make to mailboxes, etc., requires the use of the Exchange 2010 console (which doesn't support modern auth, and therefore doesn't work anymore) or editing AD attributes directly.
I have recently discovered that I can install the Exchange 2019 management tools and use the open source project Exchange Recipient Admin, which is nice.
But is there a way to move my source of authority for all things Exchange to Exchange Online and Azure AD, which still keeping Active Directory on-prem for everything else?
Not that I'm aware of. When using Azure AD Connect, the source of authority for all objects synched to Office 365 is the on premises AD. This is still something Microsoft is working on AFAIK. Their recent changes (at the link below) and with Steve Goodman's tool piggybacking off those is a step closer, but we're not quite there yet. While some Exchange things can be managed solely (and only) from the cloud side, like mailbox delegation, most everything else needs to be managed from on-prem.
https://docs.microsoft.com/en-gb/Exchange/manage-hybrid-exchange-recipients-with-management-tools