I'm half joking, but you could open neovim in your terminal, then open terminal mode in neovim, then open tmux in there and that way you get neovim navigation in your tmux session.
I just tried it and while it can jump between panes in the normal mode using vim keybindings, you have to use tmux keybindings to switch between panes in terminal mode.
Have you tried using https://github.com/christoomey/vim-tmux-navigator ? I use it for using to move between window/panes in vim/tmux.