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.
I think he looses the saber in the “fight” between him and Kylo when Ben puts him to sleep. Also I kinda really like he uses the blue saber because the green one kinda represents all his failure with Ben, so even if he hadn’t lost it I really think he wouldn’t be able to use it again, and showing him using the blue saber at his final heroic moment against Ben and not trying to attack Ben at any point, shows that Luke gives away all the pride and failure the legendary luke skywalker and his green saber represents. That Luke is the same Luke that blinded for his own ego tries to kill Ben. When he uses the blue saber represents a more young and naive Luke, a pure-hearted one we see in New Hope and Empire.
But I really think is kinda of a waste Luke don’t using both of them. Luke was like THE GRAND MASTER of new jedi, he certainly knows how to fight with two sabers.