Don't overlook the awesome "automatically bury session" option, which hides the "actual" iTerm2 window running the tmux control plane: https://iterm2.com/documentation-buried-sessions.html and this is the preference I mean: https://github.com/gnachman/iTerm2/blob/v3.5.2/Interfaces/Pr...

I also have dedicated .ssh/config entries for ensuring that ssh connects directly to tmux:

  Host whatever-mux
    Hostname whatever
    RequestTTY yes
    RemoteCommand /usr/bin/tmux -u -CC att