Claudius I just look at the prices we pay for our players, the result of extension negotiations, and the prices we receive on our outgoings. Coupled with the historical and recent reports of his waning influence within the club, a reasonable conclusion to draw might be that he's not doing anything to blow anyone away. I've been suspicious of his overall ability to move well in the market since Sanllehi days, and it seems Arteta has gotten the better of him on that front over the years. His track record is pretty poor, to be fair. He's charismatic and likeable, but does he actually get what needs doing done?
There's a reason that "what do edu do?" was a thing. You say that it's all behind the scenes, but surely the evidence of that would be visible somewhere. You ask what Bergiristain has done, but he's got the proof in his pudding. Edu, not so much. He's good a spending Kroenke's money, I'll give him that.