OP: Is Buddha Nature Vedanta's opposite of Brahman i.e. Non-Existence, Consciousness, Bliss?
Firstly, what is Tathagatagarbha aka Buddha Nature? Is it the same as or opposite to Vedanta's Brahman?
According to this article:
Tathagatagarbha, or Tathagata-garbha, means "womb" (garbha) of Buddha
(Tathagata). This refers to a Mahayana Buddhist doctrine that Buddha
Nature is within all beings. Because this is so, all beings may
realize enlightenment. Tathagatagarbha often is described as a seed,
embryo or potentiality within each individual to be developed.
And it discusses further:
In the religions of the Buddha's day that were the forerunners of
today's Hinduism, one of the central beliefs as (and is) the doctrine
of atman. Atman means "breath" or "spirit," and it refers to a soul or
individual essence of self. Another is the teaching of Brahman, which
is understood as something like the absolute reality or the ground of
being. In the several traditions of Hinduism, the precise relationship
of atman to Brahman varies, but they could be understood as the small,
individual self and the big, universal self.
However, the Buddha specifically rejected this teaching. The doctrine
of anatman, which he articulated many times, is a direct refutation of
atman.
Through the centuries many have accused the Tathagatagarbha doctrine
of being an attempt to sneak an atman back into Buddhism by another
name.
In this case, the potentiality or Buddha-seed within each being is
compared to atman, and Buddha Nature -- which is sometimes identified
with the dharmakaya -- is compared to Brahman.
You can find many Buddhist teachers speaking of small mind and big
mind, or small self and big self. What they mean may not be exactly
like the atman and Brahman of Vedanta, but it's common for people to
understand them that way. Understanding Tathagatagarbha this way,
however, would violate basic Buddhist teaching.
Another article here tries to point the origins of tathagatha-garbha or Buddha-nature to the Luminous Mind in the Pali Canon (which according to Theravada Buddhism, is not permanent or eternal, but is dependently arising - see this answer).
It comments in its conclusion:
In conclusion, when we try to interpret the thought of the
'tathagatagarbha', we should keep several points in mind:
- The 'tathagatagarbha' symbolizes the potential for enlightenment (a
principle) rather than a material "essence" of ultimate truth,
... Thus it is
better to take the 'tathagatagarbha / Buddha nature' as representing
"profound existence" derived from "true emptiness" rather than as a
monistic self.
Buddha Nature is said to originate from the concept of the "luminous mind" in Pabhassara Sutta, which is anyway not eternal, not unconditioned and not impermanent (see this answer).
Nirguna Brahman is described in Advaita Vedanta as the substratum of all phenomena in Vivekachudamani 289 and as the material cause of the phenomenal universe in Aparokshanubhuti 45.
So, while Buddha Nature is simply the potential for enlightenment (a principle), it is not the material "essence" of ultimate truth, which Nirguna Brahman is.
So Buddha Nature and Nirguna Brahman are not the same. But they are also not opposite. They simply refer to different concepts. Like oranges and apples - not same, not opposite, just different.
OP: As awareness/ consciousness is always "on", no matter of what state it's in then surely awareness/ consciousness would still
experience non-existence, akin to our lack of any experience in deep
sleep.
Awareness/ consciousness in Advaita Vedanta is always "on". This is described by Bhagavad Gita 13.14 and Shvetashvatara Upanishad 6.11.
However, this is not the case in Buddhism.
The Buddha taught the following, from MN 38:
"Just as fire is classified simply by whatever requisite condition in
dependence on which it burns — a fire that burns in dependence on wood
is classified simply as a wood-fire, a fire that burns in dependence
on wood-chips is classified simply as a wood-chip-fire; a fire that
burns in dependence on grass is classified simply as a grass-fire; a
fire that burns in dependence on cow-dung is classified simply as a
cow-dung-fire; a fire that burns in dependence on chaff is classified
simply as a chaff-fire; a fire that burns in dependence on rubbish is
classified simply as a rubbish-fire — in the same way, consciousness
is classified simply by the requisite condition in dependence on which
it arises. Consciousness that arises in dependence on the eye & forms
is classified simply as eye-consciousness. Consciousness that arises
in dependence on the ear & sounds is classified simply as
ear-consciousness. Consciousness that arises in dependence on the nose
& aromas is classified simply as nose-consciousness. Consciousness
that arises in dependence on the tongue & flavors is classified simply
as tongue-consciousness. Consciousness that arises in dependence on
the body & tactile sensations is classified simply as
body-consciousness. Consciousness that arises in dependence on the
intellect & ideas is classified simply as intellect-consciousness.
Think about it. How can the silent witness witness anything except through one of these media: eye, ear, nose, tongue, touch or mind? There was never a time, when there was consciousness being aware of something except through the eye, ear, nose, tongue, touch or mind. There is therefore no independent consciousness.
Consciousness is dependent on and conditioned upon these six media. It does not exist independently connecting all beings. The consciousness in every being may be of a similar type, but it's not the same consciousness.
For example, I can say that every candle has a similar flame, but it's not the exact same flame that appears on every candle. Each flame is different.
Awareness/ consciousness is not always "on" in Buddhism. It depends on the six sensory media.
Also useful, also from MN 38, in which the Buddha makes clear that it is not the SAME consciousness that wanders through one's life:
Then he went to the Blessed One and, on arrival, having bowed down to
him, sat to one side. As he was sitting there, the Blessed One said to
him, "Is it true, Sāti, that this pernicious view has arisen in you —
'As I understand the Dhamma taught by the Blessed One, it is just this
consciousness that runs and wanders on, not another'?"
"Exactly so, lord. As I understand the Dhamma taught by the Blessed
One, it is just this consciousness that runs and wanders on, not
another."
"Which consciousness, Sāti, is that?"
"This speaker, this knower, lord, that is sensitive here & there to
the ripening of good & evil actions."
"And to whom, worthless man, do you understand me to have taught the
Dhamma like that? Haven't I, in many ways, said of dependently
co-arisen consciousness, 'Apart from a requisite condition, there is
no coming-into-play of consciousness'? But you, through your own poor
grasp, not only slander us but also dig yourself up [by the root] and
produce much demerit for yourself. That will lead to your long-term
harm & suffering."