Is there a way to add a practitioner to an organization within the medplum app?

Yep! The resource you're interested in is

PractitionerRole

. That represents the "membership" of a Practitioner to the Organization. Right now, the Medplum App doesn't have a direct link, but if you navigate to https://app.medplum.com/PractitionerRole, you can view and create

PractitionerRole

resources