Alpicool is mentioned on the above list. I bought this one because it’s smaller than many of the coolers on the list. It works very well as both a fridge or freezer (not both at the same time). Temperature control is good. This was the best medium size option that I could find, so it might be what you are looking for.

Do you actually need a generator at all? Seems this is meant to just run directly off the car battery.

Or if you want to use it away from the car, could tether it to one of those misleadingly-marketed "solar generators" and when the battery in that device runs low, recharge the "solar generator" from your car (probably by idling in park for an hour or two).