GNOME:

    gsettings set org.gnome.desktop.interface gtk-key-theme-name 'Emacs'

or GTK:

     ~/.config/gtk-3.0/settings.ini
     ~/.config/gtk-4.0/settings.ini


    [Settings]
    gtk-key-theme-name = Emacs

I have it enabled but it can be very confusing: depending on whether you're in a text field or not, in say a browser, ^W will mean delete word or close tab. And sure enough closing a tab will sometimes but not always focus the URL box of the previous tab.

There used to be an obscure internal GTK setting to properly separate control plane from command plane like on (then named) Mac OS X but IIRC it's long gone / hardcoded to only GTK on macOS.

EDIT: Found it, GTK up to 3 had proper <Primary> vs <Control>. In what I would consider to be a fatal regression, GTK 4 just aliases <Control> and <Primary>, leaving the apps to do the work.

https://gaphor.org/2022/12/10/gtk4-macos-keybindings/