Can someone please clarify the default focus handling of the X11 server? My understanding is that the focus \'follows the mouse\' and sure enough if I move the mouse between sep
Having focus refers to the window which receives keyboard input when you press a key.
The focus handling depends on your window manager. The most common mode is click to focus, which your window manager is set to, where you only get focus when you click on the window. An alternative is that the keyboard focus follows the mouse, which is what you are expecting.
There should be a setting to change this in your window manager settings.
The cursor changing does not indicate focus, just that the terminal has defined a different cursor.
To demonstrate, open a terminal and an xev window.