Not per application, but per SQL Database Engine Instance - unless you are using these terms interchangeably. We have 4 SQL Instances. Each Instance is 'shared' so running multiple applications' databases.
SSRS has 2 components - the database engine and the reporting services. If - as you stated above - you have separate servers for each SSRS instance that has both components installed on that SSRS server then each instance of SSRS is not 'tied' to a specific SQL Server database engine. If - however - you have separate SSRS servers where only the reporting services component has been installed - and the databases for SSRS are hosted on the SQL Server database engine then you have 'tied' that instance of SSRS to that database engine.
This isn't needed - one instance of SSRS with both the database engine and reporting services components can support any number of reports that connect to any number of instances and databases. You could have reports connecting to Oracle, SQL Server, MySQL, Postgres, Vertica - or any other source system that has an ODBC data source available.
In almost all cases - SSRS is backward compatible. That means a report that was built to be deployed to a 2014 system can still be run on a 2019 SSRS instance. Ideally - you would upgrade the reports but it isn't necessary unless that specific report is failing.
The question I have now is - what license do you have for the SSRS instances? If you are not licensed for Enterprise - then scale-out is not an option. If you are on Enterprise - then I would look at converting from 4 separate instances of SSRS to a scale-out implementation.