And what is this circuit anyway? What is the relay? What are these dual stair switches supposed to be used for?
Added after 5 [minutes]: OK, I think I've figured it out because on closer inspection

. I understand this is two light circuits lit by two sets of stair switches? Then what is the electronics for and what is it actually? Because you've drawn some sort of component with marked terminals, but nobody knows what it is
Added after 4 [minutes]: O, the title also says what the contraption is

. But I'll tell you honestly, you showed the wiring diagram yourself, so what do you actually expect?
Added after 5 [minutes]: You unplug the "black" (in the drawing) wires from under the bulbs and plug them in as L1 and L2 (to the relay) with the ends from the bulbs, and to S1 and S2 with the ends from the switch. And of course L and N as power supply.