Ireland, the country with 2 center right parties that differ with regards to patronage networks and political history from 1940, is one of the most left-wing leaning countries in Europe?

Eh, ireland is unique in that it has a centre-right coalition making it de facto one party. The main opposition, Sinn Fein, is about the same size as Fine Gael and Fianna Fail and might overtake Fine Gael at some point

Right. So, no left wing party, not even a center left party, has been in power in Ireland in its history. But I'm supposed to believe that it's one of the most left wing countries in Europe?

in spirit it is, at least at its core. The irish revolution and civil war had strong socialist undertones