Initially, I had given the same roles as you tried Collaborative Data Contributor
or Collaborative Runtime Operator.
While trying to open the Synapse workspace, I saw a 403 error code:
To resolve the error, I assigned the RBAC role of Synapse Administrator or Synapse Contributor in Synapse Studio.
To do this, navigate to Manage in Synapse Studio, -> Select Access control -> click Add, Select the Synapse Administrator or Synapse Contributor, -> select the user who is accessing Synapse Studio
After assigning the Synapse Administrator role, you can perform the data copy action.
References: