I would think the primary job of a spy is to be a manager (a handler) of a bunch of traitors (including unwitting ones) in the enemy country. Any eventual assassinations would be best done through the hands of one of those subordinates.

This is more like the picture le carre paints

No, it would mean that spies don't do assassinations.

The primary job of a spy is to gather classified information, ideally without anyone noticing. Dead bodies tend to be noticed.

Actually, in all the Bond movies, I don't recall him ever having a mission to spy per your definition. Spies are typically used in situations between countries and many of Bonds foes clearly weren't countries, e.g., Goldfinger, Dr. No, Drax. They were just super criminals without allegiance to any country. The closest classic spy movie I recall was From Russia With Love but even that involved SPECTRE more than Russian.

I mean, fundamentally the spy thriller spy does anything a given country needs done in another country that would otherwise be considered illegal or an act of war, if the provenance of the order was known.

Bond was more of an assassin AND spy. A spassassin.