The square pad correctly shows pin 1 of the connector. There are two designs for the 32u4 board, the first has pin 1 at opposite ends (the layout was easier) and the later one, marked v3 on the silkscreen, has them at the same end.
Putting them at the same end was not for neatness : it's because if it's that way round, the USB cable exits from the board in the same direction as common GPIB cables. Sometimes, instruments have more space that way.
Both pcbs are the same circuit and both can be used with the same software if you don't care how the cable is routed. It sounds as though you have the earlier one and you should take the square pin 1 marker as correct for both pcb and socket.
The board should be assembled with the socket first, pushing the connector through from the unscreened side so the pins show on the silkscreened side. In fact this is the only way you can assemble it with pin 1 in the square pad. Then solder them. Once the arduino is in place you can't reach the pins.
Then fit the arduino, on header pins. The silkscreen writing should be upright and visible, the arduino with the components on top and the connector pointing upwards so TX0 goes to the square pin. As ogdento notes, pin 21 will be a bit tight.
See also
https://www.eevblog.com/forum/projects/ar488-arduino-based-gpib-adapter/msg2728612/#msg2728612I'm not sure why you think GPIB pin 1 should connect to arduino pin 4. Pin 4 is ground. GPIB pin 1 connects to arduino pin 6 (D3). Maybe you're comparing it with one of the other layouts ?
Many of the pin assignments differ between modules because the module pins themselves are different. The 32u4 version tries to assign them to maximise software efficiency. Make sure you select the correct board type in the arduino IDE as explained by WaveyDipole !