Hi Andrew,
All Raspberry Pi boards are officially documented as 5.1VDC devices, it seems a bit odd when most people can get them to work on 5VDC just fine but there are caveats and gotchas to be aware of, there was a long discussion on it in this thread which you may find relavant.
The 2-way Fast Charge Buck Module is a bit of an odd device because it is trying to use a charger as a power supply which are two very different design goals.
The first problem will be that the Pi Zero doesn’t support a fast charging protocol so it will just appear as a dumb 5V device to the charger. I suspect the display won’t use these protocols either and wants 12V.
I’m not sure that this buck module will support two different outputs, especially when neither have the protocol to request their preferred voltage supply.
What kind of power input socket does your display use? We can help you come up with a power supply solution better suited to these devices.
