In Eastern Christianity, there was a different direction. The Cappadocian Fathers, especially Gregory of Nyssa, denied that any predicate (including Being) properly describes the divine nature, which is ineffable and totally incomprehensible. Building on this, the writer known as Pseudo-Dionysius developed an apophatic theology and philosophy which placed the Trinity and the Divine nature above all names and predicates, including Being. This was to emphasize its richness but also its mystery, since Dionysius’s thought is highly mystical.
Eriugena, an Irish Philosopher, drew on this, and also placed the divine nature beyond comprehension and names, as well as making the universe a sort of manifesting of the unmanifest Being of God, which got him in trouble for pantheism.
The scholastics, especially Aquinas, drew more on Augustine and while sticking to the ineffability of God’s essence, still felt Being was the most accurate way to describe the fullness and infinite riches of the divine essence. Meister Eckhart, who tried to wed Aquinas with Dionysius’s negative theology and possibly also Eriugena’s ‘theology of glory’, with his peculiarly expressed mysticism, also got in trouble but also worked out an interesting philosophy of Being which has a lot in common with Buddhism.
With the focus on sensible reality and science in the Enlightenment and the 20th century, the idea that Being was the highest principle came into some problems, but now it is being valuably recovered.
I think Being is a useful way to understand higher reality, so long as it doesn’t become an intellectual idol. We need to recover the dialetic of Being with non-Being in my view to recover the beauty and depth of the Greek vision of Being. From this Western Philosophers can look to Asia with its treasures in considering nothingness as a metaphysical principle, without collapsing into the arid nihilism Western philosophers sometimes fell into when considering it. I think personally the highest reality is beyond either Being or Non-Being, but understanding the highest reality can be helped by a dialectical process using both terms and names derived from them. It should also help in recovering a sense of the divine mystery, which was somewhat lost in Scholasticism and its nuanced logic.