That's a SPDT switch. https://learn.sparkfun.com/tutorials/switch-basics/poles-and-throws-open-and-closed
Just ignore one pole.
Easiest is to use one gpio input for the pushbotton switch.
And one gpio output to drive the LED.
In the patch, use gpio/in/digital -> logic/toggle -> gpio/out/digital
Doing both the LED and button with a single gpio, it is possible but requires an object that does not exist yet, to switch the gpio between input and output at a high rate (so you don't see it is actually blinking).