I need to be able to launch a program in the background, make it persist after the "parent" terminal closes and be able to access its stdin/stdout from another terminal. I don't care about multiplexing.

I've been using tmux for this but I don't like how it hijacks my mouse and that i'm not able to use my terminal's search feature and have to use what tmux tui provides instead. In other words, programs launched directly in the terminal feel more comfortable to work with than when they are launched inside tmux.

I feel the ideal program should behave much simpler. Like e.g. on attach it should clear the screen, print the stdout buffer it accumulated and give me stdin prompt, that's it.