Will SSRS be extinct soon, and PowerBI the new model?
Does this mean Microsoft will eventually try to deprecate SSRS?
Ref: https://blogs.msdn.microsoft.com/sqlrsteamblog/2017/07/19/sql-server-2017-reporting-services-release-candidate-now-available/
No.
We moved Reporting Services installation from the SQL Server installer to a separate installer. This is a packaging change, not a product change; access to SQL Server Reporting Services is still included with your SQL Server license. The new installation process keeps our packages lean and enables customers to deploy and update Reporting Services with zero impact on your SQL Server deployments and databases.
Should our team try to build new reports in PowerBI and transition the previous SSRS reports?
If you need PowerBI you should start using it but not thinking SSRS being deprecated.
About the separate installer for SSRS, here's a good reason: https://blogs.msdn.microsoft.com/sqlrsteamblog/2017/05/17/a-closer-look-at-power-bi-report-server/ In summary, SSRS, and PowerBI Report Server has similar features hence it might be beneficial from the developer's perspective to group them accordingly (just a hunch, I am not a Microsoft employee, so I do not have visibility on this).
Does this mean Microsoft will eventually try to deprecate SSRS? No one knows what the future holds, so we don't know if Microsoft will deprecate SSRS in the foreseeable future. In my opinion, SSRS is a paginated report solution as compared to PowerBI which is more of a Dashboard/Analytics tool; The two still caters different types of users. So No, at this point, I do not see Microsoft deprecating SSRS.
Should our team try to build new reports in PowerBI and transition the previous SSRS reports? Look into the use case of PowerBI. As far as my experience can say if a user is repeatedly generating reports with different parameters you can consider a PowerBI Report with a bunch of slicers instead. You can also consider it if an SSRS Report is comparing historical values. But the real deal with PowerBI (Excel 2016 or PowerQUery in Excel 2013) is its Self Service nature. It allows a user to connect to common data sources and perform different transformations with minimal coding, and the output report can repeatedly be executed whenever an update has happened on the data sources.
Edit: It has been a year and right now the Paginated Reports capability is included in PowerBI (Both service and report server). From a technology perspective RDL files will not be deprecated. But from a solutions perspective the only thing that prevents Microsoft from deprecating SSRS is the licensing. SSRS comes free with SQL Server Express, while the Paginated Reports capability of PowerBI comes with SQL Server Enterprise Edition with Software Assurance (Through PowerBI Report Server) and PowerBI Premium (P1 and above).