Assuming that you are measuring the voltages correctly
there must be components between wherever you are measuring the input voltage and the "5V pin".
Nano 5.00v input via USB and bench supply shows 4.47 to 4.42v at the "5v" pin.
There is a 5V regulator from Vin to the 5V pin.
What is this 'and bench supply', where is it connected and what voltage is it ?
Since it is apparently too much trouble to google the Nano schematic, I did it for you.
Let me repeat, think it through.
Nano 5.11v input via USB and power bank shows 4.37 to 4.41v at the "5v" pin.Nano 5.00v input via USB and bench supply shows 4.47 to 4.42v at the "5v" pin.
Seriously? Think it through. Take a USB cable and cut off the big connector end and find the red and black wires.
I assume I am, I tried 3 meters and 2 usb-inline testers for the incoming voltage. The meter set to 20vdc range. Black probe to "Gnd" on the nano and red probe to the "5v," pin.