Not much to write up. This was on Arch, I just installed GNOME (on Nix now, so this is from memory):

    sudo pacman -S gnome
    sudo systemctl enable gdm
    sudo systemctl start gdm

GNOME Wayland is the default session. Log in, press the super key top open Settings, go to Display and set scaling to 200% on the 4k screen. After that, everything worked fine. Since I use the non-4k screen vertically, I had to rotate the second screen in the settings.

The last time I used Fedora it worked without extra work (besides setting scaling to 200% in the Display settings).

Things only started working well with GNOME 2.26 and very well with 2.28.

In any case, you have to make sure that you are using Wayland, support for multi-DPI screens on X.org has been terrible for me. Even a single 4k screen is not very consistent in X.org (e.g. the mouse cursor sometimes becomes tiny when moving between windows).