Difference in button state memory between Arduino Leonardo and ESP8266

Hi. I have a piece of code that works perfectly on the Arduino Leonardo while on the ESP8266 it no longer works. Here is the code:
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On the Arduino Leonardo and ESP8266 I have two cables connected to pin 4 and GND.
On the Arduino Leonardo, when I short-circuit the cables, the LED on the board lights up and stays on until I short-circuit the cables again to make it go out (it remembers the state). On the ESP the LED only lights up when the cables are shorted and does not remember the state.

Why the difference? What can be done to make the ESP behave the same as the Leonardo in this particular case?

What specific board are you using with the ESP8266? Do you have the button hooked up to D4?

Specifically, it is a NodeMcu V3 and the button is connected to D4

D4 is GPIO 2, so you need to change the buttonPin to the value 2 or D4.
Pin information: Link .

I don't know who when designing the NodeMCU came up with this "fantastic" idea of numbering the pins differently. As soon as I read the topic I immediately thought of this problem. Even more "killer" is the Wemos D1 Mini - the leads are almost like on the ESP-12, but GPIO15 has been flipped to the other side. And where GND should be is 5V.