Electronic – How is the 220V line in US different from other parts of world? Does a US 220V line need two switches for each wire

Why not consider placing your small Arduino board and its power source in the electrical box where the light bulb is located?

From your diagram it appears that the powered 220VAC feed and return line are both in the electrical box at the light fixture.

Edit to Add an Alternate Idea to try out. There is too little data regarding the Lifx bulb to know if this is even feasible at all. So you would have to simply try it.

The idea is to remove the wall switch from the AC circuit and instead wire it into the MCU board. Then wire a small transformer across the AC lines that come to the switch box. This would likely have a low turns ratio and would operate off the current that passes through the special LED bulb unit. An AC power converter on the other side of the transformer would convert AC to DC power.

In short, capacitance between the two wires is your answer.

Here's an example I faced many years ago. A friend of mine rewired his house but asked to borrow my meter before he connected ground to the pipes coming into the property. He phoned me up and said there was 115VAC measured on the unconnected earth wire and he was frightened of grounding it. (Local AC voltage was 230V and I assured him that "live" was at 230V, neutral at "0V" and the middle unconnected wire would find a voltage that was roughly halfway between the two wires (due to capacitance between conductors). He connected the earth wire and no problems.

What you are seeing is the natural effect of capacitance coupling the voltage on one wire to another in close proximity.