How do I resize the ‘usable area’ of a tmux session?

Perhaps enabling the aggressive-resize option will help:

set-window-option -g aggressive-resize

A good overview of tmux options is given here.

When attach screen you may use detach mode

tmux attach -d with will resize screen after disconnect other clients from the sessions (and someone who used small screen)

Or you can interactively detach by pressing Ctrl-B-Shift-D