vim-tmux-navigator[0] is probably the best thing I've installed in my terminal for transparently moving between splits. Using it has allowed switching splits to become so thoughtless that it's automatic as I move my eyes.
This really bothers me too. For a while, I've been considering writing a window manager (or wayland compositor) that tabs all windows by default, and provides an easy model around un-nesting tabs and tiling the new window. Something like the tabs of i3 meets the simplicity of bspwm. The idea being I can then just use new windows for applications, and have the same keyboard shortcuts and semantics for tabs everywhere.
kitty has remote control (the ability to contrl it fro scripts/shell prompt) which you can use to integrate its windowing/layouts with other programs. Not sure what else the terminal emulator could do in this space, but if you have ideas, feel free to discuss them on github
I wish this were all unified into a single window/tab/keybinding model. That was easy to code against and write your own interactions for.
I keep hoping I'll see a boundary-pushing project like Kitty do something new in this space.