The Abrahamic God is certainly awake. He even speaks to his people.
He is not enlightened.
Who is the Buddha’s God, and what did he say to his people?
What do you mean by this? Buddhism is not monotheistic, there are tens of thousands of gods:
Sakra, the ruler of the celestials, with twenty thousand gods, his followers, such as the god Chandra (the Moon), the god Surya (the Sun), the god Samantagandha (the Wind), the god Ratnaprabha, the god Avabhasaprabha, and others; further, the four great rulers of the cardinal points with thirty thousand gods in their train, viz. the great ruler Virudhaka, the great ruler Virupaksha, the great ruler Dhritarashtra, and the great ruler Vaisravana; the god Ishvara and the god Maheshvara, each followed by thirty thousand gods; further, Brahma Sahdmpati and his twelve thousand followers, the Brahmakayika gods, amongst whom Brahma Sikhin and Brahma Gyotishprabha, with the other twelve thousand Brahmakayika gods.
– Saddharmapundarika sutra, Chapter 1
The Buddha is recorded as having ascended into one of the heavens and preached to the gods there.
Ultimate nirvana is unconsciousness, which is what I meant by annihilation.
All descriptions of nirvana fall short. Perhaps the closest is by Vimalakirti:
Then the Bodhisattva Manjushri said to Vimalakirti, “We have all given our teachings, noble sir. Now, may you elucidate the teaching of the the entrance into the principle of nonduality.”
Thereupon Vimalakirti kept his silence, saying nothing at all.
The Bodhisattva Manjushri applauded Vimalakirti: “Excellent! Excellent, noble sir! This is indeed the entrance into the nonduality of the Bodhisattvas.”
– Vimalakirtinirdesa sutra, Chapter Nine
The Buddha cannot describe it as a state because it is absolute sleep, as opposed to wakefulness.
You need to read more Buddhist texts:
[The Buddha said:] “There is, monks, an unborn, an unbecome, an unmade, an unconditioned. If there were not that unborn, unbecome, unmade, unconditioned, no escape would be possible from the born, become, made, conditioned. But precisely because there is an unborn, unbecome, unmade, unconditioned, escape from the born, become, made, conditioned is possible.”
– Udana 8.3
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