You can use ZHA (natively integrated into Home Assistant), deCONZ (requires an external deCONZ or Phoscon exist), or Zigbee2MQTT (requires existing Zigbee2MQTT and MQTT). Read integration docs:
Yes all different Zigbee solutions (ZHA, Z2M, deCONZ) require you to buy a Zigbee adapter and some Zigbee solutions support many different types of Zigbee adapters while others only a few or just one.
Correct termenoloty for this type of Zigbee gateway/bridge/hub adapter is a “Zigbee Coordinator”, see:
Note that you can use different Zigbee solutions at the same time but they will each need their own dedicated Zigbee adapter and every solution will only set up a single Zigbee network and it is not possible to connect different Zigbee networks so they will not be aware of the others in any way.
No, while it shares some similarities to Bluetooth Mesh technology, Zigbee is a different specification, and regardless all different protocol specifications for WPAN (Wireless personal area network) and WSAN (wireless sensor actor networks) will need separate dedicated digital radio gateway adapters.
You will need a seperate dedicated digital radio “gateway/bridge/router” adapter for each type of wireless IoT technology you want to use, that includes; Wi-Fi, Bluetooth (Bluetooth Low Energy, Bluetooth Mesh and different versions), Zigbee, Z-Wave, Thread, 6LoWPAN/LoWPAN, EnOcean, UWB (Ultra-wideband), etc.
Recommend watching some of these videos that explain Zigbee if do not want to read more about it:
PS: Bluetooth devices are actually generally the worse to deal out of all those mentioned protocols as each manufacturer implements their own quirks and application layers on top so not standardized at all.
I have now bought a CC2531 USB, which mentioned zigbee2mqtt in the article description.
I installed zigbee2mqtt - and got stuck with the “502: Bad Gateway” error. I will continue working on this tomorrow…different topic
"CC2530/CC2531 USB stick, module, or dev board hardware flashed with Z-Stack coordinator firmware (no longer recommended as uses deprecated hardware and very old end-of-life firmware, plus will not work properly at all if the whole Zigbee network has more than 15-20 devices)"