Zigbee or MQTT - how to? (Zigbee2MQTT already installed)

I had my automation running for years using a Zigbee-Ethernet gateway, Zigbee2MQTT and NodeRed
Now I installed Home-Assistant and added both:
“Zigbee Home Automation” and “MQTT” integration configured.

For some reason, with different device count.
Also , If I disable/remove “Zigbee Home Automation” then no zigbee devices work anymore, as if MQTT integration did not work - but when thigs work, they work with the names that MQTT already has for the devices, telling me that it works with “MQTT devices” - While “Zigbee Home Automation” displays only the manufacturer/default names.
Am I supposed to have both integrations?

There are two different integrations, ZHA and Zigbee2MQTT. Z2M uses MQTT, ZHA doesn’t.