Zigbee Coordinator adapter are presented as a standard serial port so need somehow connect that serial communcation to either the ZHA integration inside Home Assistant or Zigbee2MQTT, (with Zigbee2MQTT again being a stand-alone Zigbee gateway application working like an exteral hub).
Zigbee Coordinator USB adapter obviously require a USB-interface, so the norm is to direct- attach it directly via a long USB extension cable to a computer to its OS or pass-though it to a virtual machine.
While not primarily recommended as a more expensive solution you can as an alternative to direct- attach via USB instead make or buy a network-attached Zigbee Coordinator adapter which uses a “ser2net” style serial stream server can tunnel the serial communication over TCP via “socat”. See example:
https://www.tubeszb.com/ and https://github.com/tube0013/tube_gateways
or
https://zig-star.com/projects/zigbee-gw-lan/ and https://github.com/mercenaruss/zigstar_gateways
Note however that the serial protocol that Zigbee Coordinator adapters use is not designed to be robust or fault-tolerant as they expect a direct-attached connection, this is a bad idea to try to tunnel such serial communication over Wi-Fi, but over a wired Ethernet LAN is usually stable enough.
However, long-term it should better to run Home Assistant on a Raspberry Pi or similar computer with a direct-attached Zigbee Coordinator USB adapter as that will be the most stable option. See example: