Does HA need a zigbee adaptor like zigate?

Yes you need a Zigbee Coordinator adapter if you want to use ZHA integration or Zigbee2MQTT, read:

https://www.home-assistant.io/integrations/zha

and

https://www.zigbee2mqtt.io/guide/adapters/

My recommendation as it stands today is to buy a CC2652P based USB adapter like ITead Sonoff Plus:

https://community.home-assistant.io/t/iteads-sonoff-zigbee-3-0-usb-dongle-plus-based-on-texas-instruments-cc2652p-20dbm-radio-mcu-now-sold-for-14-99/340705/

Regardless of the adapter you choose be sure to upgrade its firmware + use a USB extension cable, and plug into a USB 2.0 port or via a powered USB 2.0 hub and not a USB 3.0 port due to interference.