From the cost wise perspective ( and not only!) it is not a good practice to connect Cloud SQl to Looker Studio directly.
I would totally try use federated queries in the BigQuery or ideally a Datastream into BigQuery and then wrangle your data. This shoudl also be done ideally on replica and not on PROD DB!!
You may cause latency issues on your PROD db and huge costs spikes whhen utilizing LS report too often,
Regards
Arkady Zagdan
Bigglo.pl