Preferably best if read this first and remember to follow all of those recommendations in that Zigbee best practice guide to be able to avoid future headaches when you setup your Zigbee equipment → Zigbee networks: how to guide for avoiding interference and optimize for getting better range + coverage
You should probably do some more research regardless as FYI, Zigbee is not universal, not at all, but there are a few Zigbee implementations that do their best to make Zigbee as interoperable as possible.
At the very least read at least these:
That specific Nortek GoControl HUSBZB-1 Combo Stick is somewhat unique and perhaps a little confusing that it is really two dongles in one as it features one radio chip for Zigbee and a separate radio chip for Z-Wave, and as such you need to use different solutions/implementations for Zigbee and for Z-Wave as they have nothing in common with each other, (as you can obviously not add Zigbee devices to a Z-Wave solution/implementation like the Z-Wave JS integration is).
So, first need to install a Zigbee solution/implementation that supports the Silicon Labs EZSP protocol (which is for the Zigbee stack/firmware used on Silabs EM3581 chip inside the Nortek GoControl HUSBZB-1 dongle).
Your opinions there is Home Assistant’s own built-in ZHA (Zigbee Home Automation) integration or the third-party Zigbee2MQTT (a.k.a. Z2M) which is available as an external stand-alone or as an add-on and no matter what connects via MQTT. Those two have different pros and cons, but the biggest right now might be that the Silicon Labs EZSP protocol currently only has experimental and limited support in Zigbee2MQTT while support for the Silicon Labs EZSP protocol in ZHA is very mature/stable.
Also know that while it is not possible to migrate seamlessly between the ZHA integration and Zigbee2MQTT, if you deice on using the ZHA integration it is at least possible to get started with that Nortek GoControl HUSBZB-1 dongle and then at a later date seamlessly migrate to an other Zigbee Coordinator adapter/dongle of practically any brand and chip.
Yes, Zigbee devices can not be connected to two different Zigbee Coordinator adapters so you need to start from scratch so you should really both remove your Zigbee devices from your SmartThings Hub as well as then perform a manual factory reset on each and every Zigbee device before pairing/joining it a other Zigbee solution/implementation.
You need to look at at the manufacturer user-guide for each device to find out how to factory reset it (the process may also be called something else like restoring to default or something similar).
What NathanCu wrote it is correct as the chip inside it is old and obsolete, however if you want to do the best with that dongle then upgrade Zigbee EmberZNet NCP firmware on it + follow best practice tips:
Nortek GoControl HUSBZB-1 / EM3581 Firmware update image → https://github.com/walthowd/husbzb-firmware/
Regardless of adapter hardware follow these tips and best practices → https://community.home-assistant.io/t/guide-for-zigbee-interference-avoidance-and-network-range-coverage-optimization/515752
Including the mentioned need to try to select the best Zigbee channel for you when forming the Zigbee network → https://www.home-assistant.io/integrations/zha#defining-zigbee-channel-to-use
Best practices to avoid pairing/connection difficulties → https://www.home-assistant.io/integrations/zha#best-practices-to-avoid-pairingconnection-difficulties