I think what parent meant was that Euler spent a few decades in Russia because of the funding provided by the empire. He spoke fluent Russian, even though there was a large German-speaking community there.
But it was typical for scientists to travel far for money. Some of the Bernoullis, a family famous for mathematicians, also worked in Russian for quite a while.
Does it really matter who payed 'em and what languages they spoke?
I wonder what he would have considered himself - he spent more time in St Petersburg than anywhere else but was born in Basel and spent a good bit of time in Berlin. For what it's worth, the Opera Omnia are published by the Swiss Academy of Sciences.
People are generally associated with where you were born/grew up/attended uni, and unless he claimed to have thrown off all that, I think we can't move the goal posts. So I think the best you can do is "Swish scientist and mathematician while under decades Russian patronage" and not really Russian. I would accept it if he had forsaken his Swiss heritage or something of that sort, but he didn't. Maybe Swiss-Prussian-Russian mathematician?
