@Das Gupta, Abhijeet When you use AI studio the corresponding workspace is created of kind Hub. Hub workspace do not support Compute clusters. See the table on his page on what type of features are supported by hub workspace. So, basically this is by design, and you cannot currently use a compute cluster for this type of workspace.
Also, it looks like prompt flow only supports serverless and compute instance type compute for the flows. See this page for infra setup.
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