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Accept the battery is DC 🔋and fridge runs on AC🔌
At least with the 12v to 120v it just won't work instead of exploding
And it turns out to be an ac motor in the compressor causing the fridge and the battery to short out If it stalls on a coil. The ac motor burns up with the battery. The electronic, water dispenser, and the ice maker would probably be happy assuming it's a full bridge rectifier otherwise polarity would matter but most likely wouldn't break it.
I'm not an engineer just a guess.
So just slap a power inverter in there somewhere and you're good to go
To answer the original question, a fridge requires quite a lot of power to operate. Could be 500W. There's also power loss from the voltage conversion, so you need a battery and an inverter that are able to provide more than that - let's say 600W. Car batteries are typically 12V lead-acid batteries. 600W means 50 amps from the battery. That's a huge current. Lead-acid batteries can handle high currents for a short period of time, but high currents have a negative effect on the battery capacity. So my guess is that the fridge could work for a very short period of time.
^THIS^
Plus to add that modern kitchen stuff like that will throw on the compressor to cool the unit down with up to a surge of 1200w. Usually for 2-3 minutes as it engages the cooling pumps and moves the refrigerant.
I've run fridge freezer units off battery a few times (deep cycle lead acid, lithium/LFP)
Probably lost about 10% or more to heat.
10% worse efficiency > no refrigerator
Maybe refrigerator until the battery catches on fire!
Inverters have gotten pretty efficient. I have one for my house that's 97.1% efficient.