power bi report server data source

The work around to entering credentials each time you publish a report is to setup Kerberos authentication, and use the credentials of the user accessing the report to authenticate with your data source.

I have just been through this, and it's a bit of an effort but not too bad once you understand the concepts. Effectively, you need to set SPNs for the accounts running PBIRS and your data source, then setup delegation for the SPNs on the account running PBIRS so the end user credentials are passed along the chain. You will need domain admin permissions to achieve this, or some help from your domain administrator.

Here's a good guide which goes through it using SSAS as a source, the same principle applies for other data sources such as SQL Server:

https://docs.microsoft.com/en-us/power-bi/report-server/configure-kerberos-powerbi-reports