Using New Outlook on Windows for professional communication and productivity
Hello
Work/school account cannot be added as alias for a personal Microsoft account.
Microsoft is quite clear about it here: https://support.microsoft.com/en-us/office/add-or-remove-an-email-alias-in-outlook-com-459b1989-356d-40fa-a689-8f285b13f1f2
In order to send invites from your business account, you need MS365 business tier license, not personal or family plans.