How so? I want KDE to remember that certain programs should only open on certain screens

KDE has been able to do this for a long time.

System Settings --> Window Management --> Window Rules

Or, right click on the title bar of the window --> more options --> configure special window settings

From there, you can create a rule that forces a certain program to open its window at a certain location. And you can specify that location to be on the screen you want it to be on. Specifically set a rule for "Position", enter the screen coordinates where you want it to go, and select "Apply Initially".

(If the application isn't behaving under that rule, try adding the "Ignore requested geometry" rule as well.)