tmux has a server containing sessions containing windows containing panes. Screen has sessions, windows, and panes (which it calls regions).
I recently finally switched from screen to tmux and I found that it's pretty seamless (especially because I use vi keybinds in tmux still). Some machines at work don't have screen anymore.
Ok,makes sense. Using this terminology, I asked claude and found out how to move a shell from a standalone window to sharing 2 panes with another shell.
Incidentally, this "screen absent" is why you should always volunteer to help create base shells (programmatically via packer not by hand) - emacs and tmux are always there when I made the image.