Arduino changing output based on wire voltage
Maybe a wire coil wound around the wire could pick up the frequency. Though I won't write about this, since I don't know much about how you would measure this, and because I think, that you are looking the wrong way.
You want to switch one device with multiple switches (how these switches are operates is not important for now). You can look at how this is normally done in eletrical installations. Here the switches are all connected to your breaker box. And there is one component, that waits for trigger signals from the switches and will switch the target device (the light in this case) accordingly. So in the end there is only one place, where the light is switched: in the breaker box. The switches in the room are only triggers. The current for the light does not flow through them. Also they don't necessarily need to carry mains voltage (triggers could also be low voltage) (though it seems they are in fact just using mains voltage, for which I don't know the reason. Maybe to avoid additional voltage conversion).
So I propose the following solution: The mains wires (230V) are only connected to the light and a (suitable) relay board. The relay board is connected to the Arduino, which can act as a Smart Switch (switching via WiFi, time based or whatever). For manual switching you can connect a switch or button to the Arduino and program the Arduino to read it and control the relay accordingly.
This solution is way easier, than trying to sense the live voltage on the lines, and this will most likely make it more reliable . It comes down to controlling an relay board and reading a button/switch, both things with tons of tutorials on the web
Note: Since mains voltage is always really dangerous, you should be really really caution. Don't use mains voltage, when developing your device. A simple LED with current limiting resistir connected to the power line of the Arduino through the relay is sufficient to check the complete functionality. Only connect mains voltage, if you are really really sure, that you did everything correct