Thank you for reaching out to the community forum with your query.
It looks like you're getting a 403 error when accessing Synapse Notebooks through an API call. The error message indicates that the principal '71b82c6f-3c4b-4060-a695-61e366d4f5f8' does not have the required Synapse RBAC permission to perform this action.
To resolve this issue, a user with Synapse Administrator role needs to grant the user either of these roles - Synapse Administrator or Synapse Contributor or Synapse Compute Operator within the Synapse Studio -> Manage Hub -> Access control (i.e within Workspace) in order to perform workspaces/bigDataPools/useCompute/action actions.
Please note that Azure RBAC is used to manage who can create, update, or delete the Synapse workspace and its SQL pools, Apache Spark pools, and Integration runtimes. On the other hand, Synapse RBAC is used to manage who can publish code artifacts and list or access published code artifacts, execute code on Apache Spark pools and Integration runtimes, access linked (data) services protected by credentials, monitor or cancel job execution, review job output, and execution logs.
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