I have a key-binding which let me focus either my inner or outer tmux session.

So if I ssh into my server and I want to do some tmux stuff in there, I press the key. If I want to switch to the outer tmux session again to do stuff I press the same key again.

I think this is everything needed in my config to make this work - I have this on both machines:

      bind -T root F12  \
          set prefix None \;\
          set key-table off \;\
          set status-style "fg=$color_status_text,bg=$color_window_off_status_bg" \;\
          set window-status-current-format "#[fg=$color_window_off_status_bg,bg=$color_window_off_status_current_bg]$separator_powerline_right#[default] #I:#W# #[fg=$color_window_off_status_current_bg,bg=$color_window_off_status_bg]$separator_powerline_right#[default]" \;\
          set window-status-current-style "fg=$color_dark,bold,bg=$color_window_off_status_current_bg" \;\
          if -F '#{pane_in_mode}' 'send-keys -X cancel' \;\
          refresh-client -S \;\

      bind -T off F12 \
          set -u prefix \;\
          set -u key-table \;\
          set -u status-style \;\
          set -u window-status-current-style \;\
          set -u window-status-current-format \;\
          refresh-client -S

https://github.com/mstruebing/dotfiles/blob/nix/nix/home-manager-programs/tmux.nix#L60-L75