Maybe I can help. I used the HomeKit Controller integration, which allows you to add HomeKit devices to Home Assistant.
To add it you’ll need to reset the lamp as the manual specifies which will remove it from your current HomeKit home and make it ready to be added to a new ‘Home’ in Home Assistant.
Follow the instructions from the link I posted and the lamp will show up as a multi colour light with temperature control.
Once added to HA you have to use the other HomeKit integration to expose your HA devices to HomeKit.
Hope this helps!