Set primary smtp address of Team/M365 group

You will need a Global Admin account to perform this task.
Connect to Exchange Online via PowerShell.

Initially add desired email address to the group:

Set-UnifiedGroup -Identity "Group Name" -EmailAddresses:@{Add ="[email protected]"}

Then set that email address as primary:

Set-UnifiedGroup -Identity "Group Name" -PrimarySmtpAddress "[email protected]"