The difference between the sidereal and tropical years would probably have been discovered during prehistoric foraging times. They would have had to use, and it is known they did use, many different methods of time measurement for keeping time of year, e.g. Primitive Time Reckoning; Nilsson, Nils Martin Persson(1920). These they would have had to compare and contrast and the most stable method, the astronomical, would be primarily relied upon.
Actually, some migrating birds provide an illustration of how astronomy is used together with other methods. These particular birds primarily rely on circumpolar configurations of stars to navigate. Yet they have not been thrown off by precession so they must use other markers as well.
The day count would only require an old tree and the word of one’s grandfather.
So the Greeks, like most people in the Mediterranean, probably already knew about the difference between the sidereal and tropical years before 3,000 BCE.
The question then becomes: “ given the lack of a common standard or a practical use over the course of a lifetime — why would they by interested?” in further studying this difference?
Why would they be curious about this longest astronomical cycle of all? Thank you for the Bowen reference as it gives the answer: for prediction of effects upon the earth. Bowen says of Simplicius: “he makes no mention of the role in this transition played by prediction, that is, by the astrological use of numerical data to foretell the planetary positions and their significance for life on Earth.”