Continuity with NodeMCU on metal door
Based on what you explained, it should work. Two wires touching is the same as a push button. 16 Ohms may not be a good connection for carrying a load, but a GPIO like this is not affected by that. The voltage divider created by this would put 3.29V at the GPIO, enough to trigger the pin as high/on/1.

So the only thing we can assume is that either there is a physical issue, or the issue is in your code.

You say With the push button I have 0.674v when not pressed, and 3.24v when pressed. I suspect you have the internal pull-up enabled. Try disabling it. You have an external pull-down, so you they can conflict.

Update: Based on OP's comment, it was (likely) a bad physical connection.