The standalone data plane API was retired in favor of the centralized management plane API for deployments.
The above is consistent with what you can observe while monitoring Azure AI Studio request traffic and viewing deployments there -- the list is populated using an HTTP GET following:
https://management.azure.com/subscriptions/...subscription-id-here.../resourceGroups/...resource-group-here.../providers/Microsoft.CognitiveServices/accounts/...resource-here.../deployments?api-version=2023-05-01