Thanks for reaching here! When trying to Add Data via the OpenAI studio it asks to enable public network access and you can't connect to Cognitive Search because currently private endpoints are not supported.
This is currently in development.
As its mentioned in the document here- https://learn.microsoft.com/en-us/azure/cognitive-services/openai/concepts/use-your-data#virtual-network-support--private-link-support
Please let us know if further query.