Hey. I had the exact same issue. All roles assigned, using System Assigned Identity, vnet and private endpoints setup correctly. Bunch of 401 errors when OpenAI studio is trying to do PUT:
PUT <resource_name>.openai.azure.com/openai/ingestion/jobs/<index_name>?api-version=2024-05-01-preview
Decoding the token used by the operation it looks like it is using your (users) identity. The error message is confusing stating that the "Principal has no access to API/Operation" when in fact that is the user using OpenAi studio that needs the permission.
Fix: Grant "Cognitive Services OpenAI Contributor" on your OpenAI resource to the user account that is using the OpenAi / Azure AI Studio"