Sorry only just saw this. We do not know 100% for sure but the historical consensus is the Gita is several hundred years younger than the latest stratum of Ved

Sorry only just saw this. We do not know 100% for sure but the historical consensus is the Gita is several hundred years younger than the latest stratum of Vedic texts, well within the era of classical Sanskrit. And the Vedic language (which technically is not Sanskrit as properly that refers to the language codified by Panini, Katyayana and Patanjali.) is somewhat different but not that different. I learned the parts of the Veda that I know the traditional way just memorizing the recitation without the meaning but based on my knowledge of grammar and vocabulary I can understand about 75% and a commentary takes care of the rest.