The devices seem to be discovered fine using ZHA which was integrated with HAOS, meaning the devices itself is fully functioning.

From the add-on page, open up the Zigbee2MQTT add-on, check the log status, if below status was print out meaning the connection to the dongle was the issues.

Zigbee2MQTT:error 2024-02-22 19:28:58: Error: Failed to connect to the adapter (Error: SRSP - SYS - ping after 6000ms)

Try to update the firmware by flashing new Zigbee coordinator firmware. Connect the devices thru computer USB port and open up the the page, make sure to use serial enabled browser such as Chrome or Fox.

SILabs Firmware Builder

Next, update the configuration inside of Zigbee2MQTT add-on, include adapter and set the value to ezsp.

port: /dev/ttyACM0
adapter: ezsp

Noted, the port above can be obtained the path from HAOS from the Setting > Hardware.

Plug in the Doogle back to the HAOS host and restart!