Actually only the display is turned off (Display and backlight)
The display itself consumes ballpark 100µA on top of my head so you could leave it on, but backlight is more like 10mA
The processors continue running in background.
You can have a general overview of power consumption here:
https://community.nxp.com/thread/491575
and turn what you do not need of in your project.
Remember the kit is a prototyping tool so for sure not perfect and matching all expected use cases.
This said you could tinker your own switch looking at Rapid IoT schematic.
The docking station on/off is connected to a switch which commands the regulators into Rapid IoT


So connecting to pin 24 at the back of the kit you could turn the kit off - This is the only way I foresee you could implement rapidly a on/off button,