To achieve this you will need a tiling window manager like Sway, Hyprland, or i3 and try to use as many CLI-based programs as possible for everything else. For browsers, there are projects like Nyxt (and some others I can't remember) that allow you to use vim or emacs like shortcuts to browse around.
However most GUI apps probably won't support an all-keyboard workflow so you will still need one. Depending on what software you use, however, you could make the vast majority of your regular computing mouse-free