It looks like the relay goes into or out of the Sirai pressurestat, and a relay turns a small current into a large current. I'm not familiar with this machine, and I have seen this particular relay, and mine had similar damage. I couldn't find a replacement, and I image you'll see a smaller current at some point in the circuit. Not sure if that's helpful, but good luck!

Yes, according to that diagram it is wired to never allow the boiler to top up until the boiler pressure is at operating temp.

I add my +1 to the "Recipe for disaster" group. I can't imagine why someone did that.