Problem Definition

In the previous user management experience, an admin could just navigate to Settings -> Administrators, click Add administrators and add whoever they want. Documentation reference.

In the newer user management experience to add an org admin you go to the Directory -> Users section, click on the user's profile, click on the three dots, and click Assign organization role. Documentation reference

This can be confusing though because you might want to make someone an org admin that is not a user on any site so they don't appear in the Users list. For example, you might have a user that is a managed account in your organization but is not a user on any site, thus they don't appear in the Users list unless you invite them first which can cause confusion.

Suggested solutions

In the new user management experience, allow org admins to add other org admins even if they are not already a user on one of the sites in the organization. For example, allow the option of designating an org admin from the user's managed account profile.