the only useful thing about a smart fridge is whether if it fails.... i hope it would make a noise. One trick i used was a cheap ble temp sensor in the fridge that would report to the BLE adapter of a tasmota device that sends mqtt messages to grafana. then i would get alerts if it was open or something broken. happened a few times!
My non-smart fridge makes annoying noises when the door is open too long, and slightly less annoying noises the first time you open it after a power cut causes it to get too warm (I believe it depends on interior temp when the power comes back on?). It might make noises when it breaks in other ways, that thankfully hasn't become relevant yet
I guess connecting to home automation would be useful for a fridge that's sufficiently out of the way that you might not hear it. But for the fridge in my kitchen the noises emitted by the fridge itself are enough for me