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.