In my work, there's not much which requires updating a full HD screen at 30 fps... video calls, I suppose. Everything else updates small portions of the screen at lower rates.
There's a program called drawterm which implements Plan 9 graphics devices on Linux. You run drawterm locally, connecting to a Plan 9 system, and your applications on the Plan 9 system draw to your drawterm window over the network. I regularly run it at 4k and it performs quite well.
I'm guessing these applications do not have any kind of animations or smooth scrolling? That would be a simple test, make your web browser or your image viewer fullscreen in 4K and see if there is lag in the scrolling/panning/zooming.
There's a program called drawterm which implements Plan 9 graphics devices on Linux. You run drawterm locally, connecting to a Plan 9 system, and your applications on the Plan 9 system draw to your drawterm window over the network. I regularly run it at 4k and it performs quite well.