Once you’ve sorted out the power source, you need hardware to drive the Raspberry Pi. You have a two options here. You can either use a PoE enabled HAT, such as the Pi PoE Switch from Pi Supply, or you can use a USB PoE adaptor, such as this one.
Finally, you need to ensure that you are using proper network cabling. Assuming you are using CAT5, CAT6 or CAT7 cables (that are using all cable pairs) you should generally speaking be fine.
In short, nothing. Screenly will not be able to tell the difference. If you however are using the Pi PoE Switch, it would be recommended that you set the jumper cable on the board such that it will automatically boot without having to press the power button.