You can currently only have one instance of the ZHA integration per Home Assistant installation, that is for sure. So for now it will only be the first instance of ZHA that you choose to configure that is used.
The only way I can think of getting two working instances of the ZHA integration per Home Assistant installed today would be the hacky option of manually copying the zha component to a new folder/directory and edit the manifest JSON file on the second copy so that its domain and name is named something else which is unique, which in practice would make it into a completely separate integration component, (and doing so would currently mess up the USB/Zeroconf discovery function for initiation the initial config flow).
I think that this pull request suggested for new introduction in ZHA documentation does explain this about current ZHA limitations → https://github.com/home-assistant/home-assistant.io/pull/24494
That might change in the future if the ZHA developers work on a ZHA WS (zhaws Websocket Server) project is continued and comes to fruition, see https://github.com/zigpy/zha-websocket-server/ and https://github.com/zigpy/zhaws-addon + the beginning of a matching thin frontend client component https://github.com/dmulcahey/home-assistant/tree/dm/zha-ws (which is the basis for a similar client-server architecture model that the existing Z-Wave JS implementation uses in Home Assistant).
For now what most people do instead as a workaround/solution to get two Zigbee gateways is to just install Zigbee2MQTT and use as a second Zigbee implementation → https://www.zigbee2mqtt.io
Regardless, a Zigbee device can only be connected to a single Zigbee network / Zigbee Coordinator.