Low-side MOSFET: Current seems limited
Perhaps your bench supply doesn't have enough current. If you use your bench supply to power the Raspberry Pi directly, does it power it correctly? If you also power the Arduino at the same time, do they both work? The RPi wants around 700 mA with graphics and Ethernet on, and the Arduino anything between 20 and 200 mA depending on load.

If not that, then I think you wired something wrong -- either the IRLB8721 (which is a great N-channel FET IMO!) source/drain (or gate, even) mixed up, or the Arduino pinout mixed up.
Or perhaps you forgot to configure the Arduino pin as output? By default, Arduino pins are inputs, and if you "write" to them with digitalWrite(), you turn on a very weak pull-up (about 20-40 kOhm) so it may "seem" to be an output.

Use a scope or multimeter to probe each voltage while the circuit is actually running, and report back!