I am not sure it is mDNS but based on the below log excerpt it seems like it may. The lamps are all in the LAN no segmentation flat network. It is a pfSense firewall.
ERROR Error resolving IP address of d.local. Is it connected to WiFi?
ERROR (If this error persists, please set a static IP address: https://esphome.io/components/wifi.html#manual-ips)
ERROR Error resolving IP address: Error resolving address with mDNS: Did not respond. Maybe the device is offline., [Errno -5] No address associated with hostname
Now that is the question, I have never been entirely clear on that. It should pop up in the dashboard and ask if you want to adopt it, but if it doesn’t do that, I am unsure what you should do next.
I would guess it has a preset api key but if not you can add the config in esphome and modify to whatever.
I would go to esphome dashboard >> add a generic config file >> modify file to match the kauf bulb >> set the use_address and attempt to flash ota
ota flash may require password but just like api key I presume this can be found somewhere on Kauf website or in documentation that came with the device.
Does it have a web interface you can access? Those details may be there or accessible in a log from the devices web interface