When changing the database in SQL Reporting Services, you can sometimes get an error in the Report Server Database Configuration Wizard around applying connection rights.
This is because the account used to enable the connection to the database doesn’t have the right level of permissions in SQL Server.
To fix this, connect to the SQL server and ensure that the service account used to set up the connection has permission to read and write to the database. For me, this was already the case, so I made the account a sysadmin. This is really bad practice, but enabled to me ensure that my issues applying connection rights in Reporting Services was definitely a security rights issue in SQL. Because my reporting server was set up as a test, there was no need to tighten the security to find the minimum level of security to fix the error applying connection rights in SQL Reporting Services.