How would a buddhist respond to the following Vedantic responses to the Buddhist critique of the atman?

The following are some arguments I came across from Advaita vedantists in some online forums against the buddhist view of the self. I am curious as to how Buddhists well versed into the philosophy would respond to them. **Buddhist Perspective on Self** > The Buddhist denial of Self is based on a misunderstanding of what > Advaita means by Atman. Atman is not a separate, individual entity but > the very essence of consciousness itself. The Buddha’s teaching of > No-Self (Anatta) was primarily aimed at refuting the notion of a > permanent, unchanging individual self, which Advaita also rejects. > > Advaita agrees that there is no permanent individual self, but asserts > that there is an underlying, unchanging consciousness (Brahman/Atman) > that is the substrate of all experience. This consciousness is not > separate from the world but is its very essence. > > The Mandukya Upanishad and Gaudapada’s Karika demonstrate that waking, > dream, and deep sleep states all require a conscious witness that > persists through all states. This witness-consciousness is what > Advaita refers to as Atman. **Arguments Against Atman** > The Buddhist argument that the Self is a mental abstraction fails to > recognize the self-evident nature of consciousness. As Shankara points > out in his commentary on the Brahma Sutras, the existence of the Self > is self-evident and cannot be denied, for it is the very basis of all > denial. > > The Buddha’s reluctance to explicitly state “There is no self” can be > seen as an acknowledgment of the problematic nature of such a > statement. If there truly is no self, who is it that realizes this > truth? Who attains Nirvana? > > Advaita agrees that the idea of an individual, separate self leads to > suffering. However, it posits that the solution is not to deny the > Self altogether, but to realize one’s true nature as the universal > Self (Brahman). > > The Buddhist critique of “me” and “mine” is valid for the ego-self, > but not for the universal Self of Advaita. Realizing one’s true nature > as Brahman leads not to selfishness, but to universal love and > compassion, as seen in the lives of great Advaita sages. **Conditioned Genesis and Dependent Origination** > Advaita acknowledges the validity of Dependent Origination at the > empirical level (vyavaharika satya). However, it points out that the > very recognition of this interdependence requires a consciousness that > is not itself part of the causal chain. > > The 12-factor formula of paticca-samuppada is a brilliant analysis of > the cycle of samsara. However, Advaita asks: Who is aware of this > cycle? The awareness of the cycle cannot itself be part of the cycle. > > The Buddha’s rejection of soul-theories is understood in Advaita as a > rejection of limited concepts of self, not of consciousness itself. > The “correct approach” described in Buddhism of seeing things > objectively without mental projections is precisely what leads to the > Advaitic realization of non-dual awareness. > > In conclusion, while Buddhism provides valuable insights into the > nature of reality, Advaita Vedanta offers a more comprehensive > framework that accounts for both the changing phenomena and the > unchanging awareness that is their substrate. It is this unchanging, > ever-present consciousness that we call Brahman or Atman, the > realization of which leads to true and lasting freedom.