I've discovered how to get the task-aware debugging information on MCUXpresso IDE running under Linux.
To get to the selection window, click on the MCUXpresso's "WIndows" drop down and then click on "Show View". In "Show View", click on "Other" and then in the "Show View" window that comes up click on "MCUXpresso IDE FreeRTOS" and select what you want to see:

This is the same/different to Windows where the debugger information works the same, but seems to come up automatically for Windows.