Pairing ZigBee devices to Home Assistant Green with SkyConnect

@Lowell What computer/appliance are you running Home Assistant on and how exactly are you physically connecting the Home Assistant SkyConnect dongle to it? And what Zigbee gateway solution are you using with the Home Assistant SkyConnect dongle, the built-in ZHA integration or Zigbee2MQTT?

Regardless, you need to be aware Zigbee is extremely sensitive to EMF/EMI/RMI and the two most infamous sources of interference comes from Wi-Fi radios and USB 3.x ports/devices/cables so make sure you are connecting the Zigbee Coordinator via long USB extension cable and connect it to a USB 2.0 port and not a USB 3.x or USB 4.x port (so connect it via a powered USB 2.0 hub if your computer/appliance that runs Home Assistant only have USB 3.x ports).

It is quite common that a compatible Zigbee device will not pair/join due to EMF/EMI/RMI interference.

Highly recommend that you read and follow this → Zigbee networks: how to guide for avoiding interference and optimize for getting better range + coverage

+1 to all of that, and take note that some but not all Zigbee devices will reset themself when you are entering them into pairing/joining mode if they have previously been paired/joined to an other Zigbee gateway, so do try to follow the manufacturers instructions manually factory reset that specific Zigbee device or at the very least remove it from the previous Zigbee gateway that it can connected to before (which will hopefully reset the device) before trying to pair/join it to a new Zigbee gateway.

By the way, if you do get a device to successfully pair/join but it does not show all entities you expect then could be that it uses non-standard Zigbee clusters and/or attributes and in that case, it could be that it needs a custom device handler (quirk/converter). If using the ZHA integration then see https://www.home-assistant.io/integrations/zha#how-to-add-support-for-new-and-unsupported-devices (or if using Zigbee2MQTT/Z2M then see → Support new devices | Zigbee2MQTT)

Unclear what you meant there but you can not connect one Zigbee gateway to a other Zigbee gateway.

FYI, Zigbee devices can not be connected to two Zigbee gateways, only one, and the Home Assistant SkyConnect combined with a Zigbee gateway implementation like the ZHA integration is a gateway.