No, synapse studio is the only place where you can create notebook, connect to spark pool and run the notebooks.
In Azure data studio, however it should be possible to connect to SQL pools and run T-SQL code
You may post the feedback in below link. These are monitored by product team and taken up based on priority and votes
https://feedback.azure.com/forums/307516-azure-synapse-analytics
Please don't forget to Accept Answer and Up-vote if the response helped -- Vaibhav