I actually migrated away from tmux because I became tired of using one set of keybindings to manage my terminal windows, panes and splits, and another set for my file buffers inside Emacs. Now I run my terminal emulator inside Emacs so I get the same keybindings for file windows and terminal windows.
I wonder if something similar to this vim plugin exists for emacs: https://github.com/christoomey/vim-tmux-navigator. Or you could maybe vibecode one yourself now.
I've used it for years to have consistent keybindings for movement across vim windows and tmux panes. Worked much better than trying to do terminals inside vim.
I actually migrated away from tmux because I became tired of using one set of keybindings to manage my terminal windows... and another set for every other os window. I also wanted gui apps being part of the session, not just terminals.
So claude and I grew the replacement over the course of a few months. Really happy with it. Never looked back.