What does tmux control mode do in practice? I use both (iterm2 and tmux), but not for this specific reason. I have just used both as a default for a long time.

So, what magic am I using without realizing it?

tmux metaphors are implemented in gui. tmux tabs are iterm2 tabs, tmux windows are iterm2 windows, etc. attach/detach and so on will restore layouts.

i believe the session can even be shared with a normal tmux session.

Yes, this was such a nice feature when I used a Mac. And indeed the session seamlessly works as a normal tmux session. I believe WezTerm does tmux-style terminal multiplexing, but doesn't integrate with tmux.