Upon installation LG's app helpfully informed me that to be notified that my LG refrigerator temperature is high or my washer's cycle is complete I am expected to inform a Korean company of my exact location at all times. The reason LG gives for this bullshit is "analytics". There is no way in hell.

I disconnected my LG appliances from wifi, deleted their spyware from my phone and duplicated the functions with Home Assistant. A couple of inexpensive sensors and a power monitoring plug provide almost all same functions without getting Korea (or the Internet) involved at all. Surprisingly this setup is much more reliable than LG's spyware too.

Or the old fashion way, don't BUY them.

First thing I do when I get a smart appliance is scan it with nmap.

A wonderful habit. I will try to copy it from you :)

About your main question, I can only guess that it's for the initial setup of these appliances. Initially, they know nothing about your Wifi situation. So maybe they open up their own Wifi and connect their app so that you can enter some info. Afterwards, maybe some services continue to run there...

Maybe for mDNS so the app can discover the appliance.

If you want your fridge to tell you its temp, just slap your own temp sensor in it. Put a mic by your laundry machine to detect the buzzer and alert you. DIY all the things, don't give these "smart" appliance companies money to spy on you.

You mention it’s listening on port 53, but have you actually tried DNS queries to see how it responds? Will it resolve www.google.com or <reverse_ip>.in-address.arpa?

Most appliances connect using a cheap microprocessor like an ESP-32 which provides both WiFi and BLE.

If there's a DNS server running, it's usually for mDNS/ZeroConf service discovery. Usually so it can easily get provisioned via a smart speaker or hub.

More details here: https://circuitlabs.net/dns-server-and-dns-sd-implementation/

The only thing LG makes that's of any value are OLED-panels. The TVs they build around them however suck ass now.

For those who are saying I shouldn't have bought these half-baked smart appliances, I agree. But I wasn't always this aware of the privacy issues involved. The washer and dryer were purchased before I grasped how problematic cloud-connected always online IoT devices are, and as mentioned in the OP the ability to tell me when my laundry was done seemed like a genuinely useful feature. In the case of the fridge it was an emergency replacement and we took what fit the preexisting niche in our kitchen, and the complete lack of output on the fridge itself necessitated the app.