Will SSRS be extinct soon, and PowerBI the new model? I read SQL Server 2017 will now include PowerBI Server. They also moved SSRS to a different installer, so it will not come packaged in the original SQL Server installation. Does this mean Microsoft will eventually try to deprecate SSRS? Should our team try to build new reports in PowerBI and transition the previous SSRS reports?
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.