For me it works perfectly with MQTT.
Did you configure your broker (mosquitto) already?.
The docs are pretty good:
MQTT - Home Assistant (home-assistant.io)
If that’s done connecting NUKI is easy.
The host (in the NUKI config) needs to be the HA compute IP Address and user / pwd as well (if you did the MQTT config properly).
I don’t know about your error messages, but I assume it’s from the APP?
So, I guess MQTT needs to be setup properly first.