Ah you mean a connection inside Unity Catalog, that wasn't really clear from the starting post. 
I've done all of this with Terraform, so there must be an API available for it. Here it is: https://docs.databricks.com/api/azure/workspace/connections/create.

For creating a Databricks to Databricks connection, you'll have to either set Unity Catalog permissions or remove the catalog isolation in the workspaces.