But how many of these Orthodox countries have been Orthodox countries officially for more than a few decades? I’m struggling to think of any besides Greece.
Lebanon never got communism and the country was founded as largely a Catholic and Orthodox project, but it still has considerable corruption. (Not defending the OP's claim, just offering another data point.)
But the question is concerning studies done recently, not centuries ago. So I think the only way to determine if Orthodoxy leads to "more corrupt" states would be to analyze one that wasn't something un-Orthodox (e.g., socialist Yugoslavia) for the last half-century.
Huh, Orthodoxy is very old and widespread. Ofc during Communism, it tended to be suppressed, but as a bedrock of the society, Orthodoxy definitely prevails in Serbia, Rumania, Bulgaria, Macedonia, Belarus and Russia at least.
Ukraine is more complicated, a nation sewn together from very different regions; Greek Catholics are an important minority, mostly present in the formerly Austro-Hungarian western part of the country, which also seems to be the most nationalist one.
Presumably these studies have been done recently, not two centuries ago, so I'm not sure how useful they are in determining that Orthodox states are "more corrupt."
I am not sure either, but I wouldn't rule it out either. Caesaropapism was probably, on the net, a negative shaping force in societies which indulged in it.
In the world of Islam, the Shi'a system of ayatollahs is structurally fairly close to Christian Orthodox Churches, and the Iranian theocracy which builds on it is corrupt beyond belief.
That said, it probably makes sense to study why some countries are somewhat less corrupt or how they managed to keep corruption in check. Corruption seems to be fairly widespread across space and time, one of the universal blights of mankind.