Please refer to this document for the explanation on GSA.
The illustration below reflects on how Looker Studio connects to GCP Bigquery with the GSAs, without having to manually generates the service account key.

Before you change the BigQuery connection on the Looker Studio Dashboard, you will need to have a GSA created with the correct permission granted to access the data for the dashboard.
Looker Studio's BigQuery connection can only work with GCP and Looker Studio within the same organization. The connection changes can only be made by that person granted with the "Service Account User" to that specific sa-looker GSA. |
Looker Studio Users are advised to use Google Cloud Project Service account to bind with the Looker Studio Project as illustrated below:
# | Description | Remarks |
|---|---|---|
| 1 | Edit the existing Data binding account. Go to Looker Studio → Data → Click Edit (as illustrated in the print screen on the right) | |
| Click on the "Data credentials" | ||
Choose the "Service Account Credentials" and fill in with the target service account. (Click Update button to update the config) |
The GSA used for Looker Studio will not require to create a user-managed service account key.
Therefore, you do not need to rotate the GSA key.