It is good to automate the deployment of PBIX files and update the data source connection string in the Power BI Report Server:
PowerShell with the use of REST API:
Invoke-RestMethod would be to deploy the PBIX.
Updating of the data source is done via the /API/v2.0/DataSources API endpoint.
Alternative approaches to all the above can be:
Deployment with RS.exe.
Modify SQL/SSAS connections using XMLA scripts.
Automation Tools:
Power Automate for scheduling the operations.
Azure DevOps or Jenkins is used for the CI/CD pipeline.
Of course, proper authentication must be ensured due to changes in a staging environment before deployment. Do let me know if you need scripts as examples!