API schemas and test suites are usually stored as code in some sort of SCM. I googled "postman maven" and "postman gradle" and found nothing official so I guess they have nothing except stand-alone workspaces.

API registry is a useful tool with modern love for nanoservices when a team of five somehow manages ten of those but I don't see anything similar done by Postman. Two of the service registries I know of were implemented in-house for obvious reasons.