The ZHA integration does cureently not have a distributable architecture (client-server model), probably Zigbee2MQTT is you best option today if that is what you are looking for as your primary requirement.
Suggest migrating your Home Assistant instance to a virtual machine (e.g. VM running Home Assistant Operating System image) on your unraid server and then run Zigbee2MQTT on the Raspberry Pi.
Recommend CC2652P based Zigbee Coordinator for Zigbee2MQTT, and maybe consider a network-attached variant (uses Serial-over-IP) if planning on running it on NAS or server-hardware that can not be located in the center of your house (for example check out adapters from TubeZB hardware for North America and/or ZigStar hardware in European Union).
Regardless suggest read and follow these related guidelines → Guide for Zigbee interference avoidance and network range/coverage optimization