Zigbee group (a.k.a. “Zigbee Light Groups”) and Home Assistant group (a.k.a. “HA helper groups”) is not the same thing. You need to create a Zigbee group in the Zigbee gateway application/integration (e.g. the built-in ZHA integration or Zigbee2MQTT), and not just a group in Home Assistant, that way the devices will be connected at the Zigbee level.