On one of my computers, the status bar has buttons to open/close the structure
and messages/log file areas in the editor. On the other, it doesn't. Does
anyone know how to adjust this setting? I feel like I've looked everywhere!

They are not configurabe. Are you using the same version of TXS on both
computers?

And they should always be there (from the time, they've been implemented).

Ah yes, pretty silly of me. I updated and the buttons are there. Thanks!