I'm trying to export data from an arduino through a USB port on a power supply module on an arduino. However, after doing some research, it seems like this isn't possible.
And not only that, it isn't a power output, it is a power input!
It allows you to feed 5 V into the breadboard, but you need a male to male cable to connect to it. The 5 V regulator on the "Breadboard Power Supply" cannot supply more than one or two hundred milliamps, depending on what voltage you supply to the "barrel jack" - same situation as on the UNO or Mega 2560 - so as with those Arduinos, the "barrel jack" input is pretty useless.
But you can use the aforementioned male to male cable to connect it to a USB "phone charger" and provide up to perhaps an Amp of 5 V power to a breadboard. the 3.3 V regulator only has to drop 1.7 V so it can probably provide up to 400 mA.
The "Breadboard Power Supply" you cite (link corrected) is substantially over-priced (compared to Aliexpress) considering its actual utility.
Not sure what you mean by "trying to export data from an Arduino" but it should be pretty obvious that this module has no data connections. What is is you are actually wanting to do?