I "think" I found the solution...
I went to the Azure Active Directory Connect Health page:
https://entra.microsoft.com/#view/Microsoft_Azure_ADHybridHealth/AadHealthMenuBlade/~/QuickStart
Click Sync services in the left menu. Select your domain/service name. Select the old V1 server, and delete it, leaving only the server running the updated AAD Connect.
The warning to upgrade that was on the top of the Connect Health page disappeared after I did that. Hoping the emails stop now (can't say if this will help - too soon to tell yet).