Luke just didn’t know the saber was destroyed. He wasn’t in Snoke’s throne room. Everything about the projection was designed to anger Kylo more. And Kylo was clouded by his anger, and unable to think about the saber’s destruction.

I think the scene would’ve worked just as well with the green saber, just think both would’ve made Kylo think about it too much and realise it wasn’t real.

With Luke giving Rey Leia’s saber, I wonder if he got rid of his Lightsaber between the destruction of the temple and his arrival on Ahch-To.