you can absolutely power via usb. sending/receiving midi messages over usb is not possible with the code as is, and i think with the nano in general. The nano uses that usb connection basically exclusively as a means to send code to it if that makes sense.
An uno or mega have the ATmega16U2 or ATmega8U2 which are a second, smaller microcontroller on board. This allows those boards specifically to be configured to use the main MCU over TTL UART and also act as a USB COM port. During normal operation, the 16U2 is just a usb to serial bridge but you can program it to be usb midi to serial bridge.
Its def out of the scope of a “simple” controller though!
Other microcontrollers like the teensy make midi over usb more possible.