A big power bank would be best. It will run the fridge for longer.
Fridges only run part of the time. They can run nearly continuously in really hot weather or hardly ever in cold weather. A higher room temperature will make them run for longer, too. A quick search suggests using 1/3 as the amount of time a fridge runs during a day, so 8 hours.
For an average 6 foot high fridge, power use will be around 500 Watts. So if it runs for 8 hours per day it will use 4000Wh. This is an estimate, if you have or can get a Kill-A-Watt meter or similar use that to check how much power is being used by your fridge.
4000Wh is a lot of battery power. This power station
www.jackery.com/products/explorer-1000-portable-power-station has 1000Wh of stored power and costs over $1000.
If you have solar panels that can recharge a power station then this works out better, the power the fridge uses is supplied by the sun during the day so the battery only uses power at night. Next day the sun recharges the battery while it also powers the fridge. The above power station would probably keep the fridge cool IF the sun was shining during the day.
Or you could recharge the power station by idling a vehicle and connecting it to the vehicle's battery. Maybe idling the vehicle for 10 minutes every hour would keep the power station charged up, I'm not sure without some numbers.
An alternative is running an inverter off of your vehicle's battery. Plug the fridge into the inverter, start the vehicle and let it run it until the fridge cuts out because it is cold enough. Repeat every hour or two or three depending on how hot it is.
Or have a lot of frozen water bottles to put into the fridge when the power goes out. This will keep it cold for a while.
Generators are used for fridges and freezers because they provide constant power and are much cheaper than most other methods. But as you say, they are noisy and fuel supplies will get used up.
Having a smaller fridge which you can use when the power goes out will reduce the amount of power required. Move the food from the big fridge to the small one and a smaller power station will do.
Or maybe a camping fridge.
This is why I don't store a lot of cold or frozen food supplies. It is difficult to provide the power needed for any length of time and once the food heats up it must be used quickly.
There are other power stations, Goal Zero, Bluetti and others make them, but all are expensive IMO. A couple of car batteries wired up together might be cheaper but more difficult to maintain.
For more info, have a look at the label on the back of the fridge and post the Volts and Amps numbers, or post the brand name and model number.
Hope that helps.