I'm still confused about the answer to the OP's question. Is it possible to implement Zigbee on a Rasp Pi Zero W with no additional hardware, or not? If not, what is the most cost effective hardware that I need to add?
You need at least a Zigbee module to connect directly through the Pizero serial or the USB port and I will suggest another 3.3V power source.
Basically this is what you need.
But only one Zigbee module won't do any good. You need to have other wireless peripheral using these modules. The module could be stand alone because the Zigbee module could have GPIO and could be directly control via software or directly from another zigbee module.
Analog In are available, Analog out are PWM pulse.
I did buy a long time ago a Zigbee shield from Italy but I don't know if it is made anymore. This particular shield has the nRF24L01 plug-in also.