Hi dear readers!
I use 2 plasma sessions at work. It is very convenient to switch between them by using ctrl+alt+f1 and ctrl+alt+f2
But I have a problem that when I switch to other session. The apps in current session get to halt.
For example if I build my C++ app with make in current session and switch to other session. The building pauses until the comeback to the session.
How to make apps to keep running in not active session?

Are you really starting two kde sessions ? Are activities not a better solution ?

I'm not sure what's happening in your setup, but it doesn't match my experience. From what I understand, there's no mechanism which somehow pauses/suspends running processes associated with one session when you switch to another (using ctrl+alt+F1, F2, etc. or using the user/session switching functionality provided by Plasma).
(there are several ways you can verify this, including playing music in one session which you can still listen to while in the other session (though the music may pause/blip briefly while switching), or using scripts which do something you can monitor from the other session).