Witness the curious fact that when most of us 1st heard “GW wasn’t really 1st”, it was pointed out that John Hanson was - under the Articles of Confederation (again, legislative). Apparently now the definition has expanded further. I gather from your Hancock reference you mean the presidents of the previous Congresses, which would mean the 1st was Peyton Randolph, not Hancock.
As it is, the President of the United States is completely different from the president of the Congresses (legislature). The factoids about the “1st president” trying to sound more cunning than all of us who only heard “GW” in class are really very moot.
Peyton R. would have a claim, but the US wasn’t independent then, was it?
If we became independent with the D of I, at the end of the meeting it was Hancock. Hanson has a claim too, for he was the first President of a “perpetual Union”. GW was the first President under the current Constitution. Not a bad thing, not a bad thing at all, esp. having served as President of the Constitutional Convention that worked to write said Constitution.
The separation into Judicial, Executive and Legislative was a significant innovation of the current constitution. UK Parliment still has the Prime Minister elected as just another legislator, and he selects his cabinet from other elected legislators.