Now that is has been determined the device is a refrigerator, I am even more leery of the wiring. I have a 1950s Westinghouse refrigerator that consumes 500 watts when it is running. Since it is newer technology than this 1940s refrigerator, I can only presume mine is more efficient and draws less power than this one.

I can see the nameplate above the door well enough to identify that fridge as a General Motors Frigidaire. Additional evidence is the ice tray insert at the left end of the countertop. Iceboxes can't make ice cubes.

No, that extension cord was not code-compliant then, any more than it is today. One or two outlets per room would have been enough to comply with the 1937 National Electrical Code, and they didn't need to be anywhere near the countertop. The 1940 code was the first to require a dedicated 20 amp circuit for kitchens, something that had been advocated as best practice since the 20s, but WW2 delayed implementation.

Not that I'm advocating it, but I can think of scarier things to plug into a light socket adapter than a 1/8 horsepower fridge compressor.

The electrical tape around mains wiring that is stapled to a wooden cabinet, and disappears under the cabinet to who knows where is a good part of a recipe for a fire. Being near water compounds the available dangers. I would hope that is a real ice box for storing blocks of ice, and not the kind with a compressor, that might be powered by the aforementioned disappearing wiring.