Unexpected voltage with wall switch off but only when nearby light switched on
This is called phantom voltage. When a cable is powering a device a field is generated, this field then induces a voltage on any wires in close proximity to the live wire. There is no problem here, this is related to how transformers work. I have seen phantom voltages close to the line voltage where there is a long run of multiple cables in parallel. The higher impedance the meter, the higher the voltage will be displayed. Their are low-Z or impedance meters that load the circuit enough to dampen the phantom voltages. But low-Z meters are not as sensitive for accurate measurements of electronic circuits so they are somewhat uncommon. I would not worry.