My parents built a house in the mid 1960s that had a similar low voltage lighting system. The main control panel was in the master bedroom and had things like all external garden lighting on or off, and I assume they could control inside lights also but never saw them use it for that.
From a technical point of view it's not a complex system to control from an arduino, but building it, installing it, and interfacing will be a mechanical and electrical challenge. The arduino part would have to stay in the basement near the main control box. Each light circuit you wish to control with the arduino would require two SPST relays (one to turn the light on and one to turn it off) as you need to generate short pulses not steady states to control the existing latching relays in the main control box. You would wire your two new relays to each of the three wires that the manual switches wire to in that wiring drawing.
Lefty