Shankara's Advaita Vedanta beautifully harmonizes all the great philosophical traditions that came before it. Due to this, Advaita shares many similarities with Mahayana Buddhist doctrines like the "Two truths doctrine" of Nagarjuna (the greatest Buddhist philosopher of all time) and the Buddhist philosopher Dignaga's "Vijnanavada". Because of these similarities, Shankara was even criticized as Prachanna Buddha (Buddha in disguise) by the traditional Hindu philosophers. Similarly, Advaita also shares many similarities with great traditional Hindu philosophical schools of thought like "Yoga", "Sankhya", "Nyaya", and "Purva-Mimamsa".
In reality, the Advaita doesn't refute other philosophies but just brilliantly supersedes them. Advaita has fundamental metaphysical and ontological superiority compared to all the previous philosophical explanations of reality given before. If you consider Einstein's general theory of relativity and Newton's Law of gravitation, Einstein's model explains gravity better than Newton's. But Einstein's model doesn't refute Newton's law of gravitation it just supersedes/refines it. You can still derive the Newtonian gravitational model from general relativity by making two simple assumptions. Newton's model still holds in the majority of cases and is widely used. Just like that Advaita explains reality better compared to other philosophies.
Now let's see where Buddha comes in on all this. Buddha was against complex philosophizing. Buddha keeps on insisting not to waste time discussing the ultimate nature of reality, he asked his disciples to just follow his teachings and get enlightened and realize it themselves.
For many questions related to the nature of reality, Buddha refused to answer (Buddha's noble silences). It is not because Buddha doesn't know the answer, but the answer cannot be logically presented in language. It can only be realized. Language and logic belong to the transactional/relative realm of reality, just like the water in the dream is useless to quench thirst in the waking world, language and logic are useless in accurately describing the absolute reality. If we want a 100% logically correct explanation for absolute reality, none of the philosophies can provide that. This is why even after his enlightenment, Buddha deliberated for some time thinking about whether he should teach what he realized at all.
So the natural question one would ask is if Buddha's initial teachings are enough for enlightenment and none of the philosophies can describe the real nature of reality, what is the need for any later development of Buddhist philosophies after Buddha (Collection of these later philosophies branched out as Mahayana Buddhism) and most importantly even after the development of very sophisticated Mahayana Buddhist philosophies why you needed a philosophy like Advaita.
Let's tackle these questions one by one. The reason why Buddha's initial teachings were later expanded is that Buddha's initial teachings have dangerous consequences if you grasp them wrongly. Greatest Mahayana philosopher Nagarjuna compared it to picking up a snake by the wrong end. Buddha's teachings presented two dangerous problems, first problem is Buddha's Nobel silence is interpreted by sceptics of Buddha as he doesn't know the answer or he isn't truly enlightened. So Buddhism ran into the risk of being easily dismissed after Buddha's lifetime.
500 years after Buddha, Nagarjuna tried to clear this scepticism by interpreting Buddha's silence philosophically and trying to show why Buddha's silence was the correct answer to those questions. He argued reality, including ourselves and everything we know, is essentially empty; there is nothing. This system of Mahayana Philosophy is called "Madhyamaka (Shunyavada)". 400 years after Nagarjuna, the next prominent Buddhist philosopher Vasubandhu came forward with another main philosophical system of Mahayana Buddhism, the "Yogacara (Vijnanavada)" which suggested, as Nagarjuna said external objects are unreal but the mind is real and that objects which appear to be external and material are in fact ideas or states of consciousness. Yogacara is considered the highest peak of Buddhist philosophy to this day. This is where the story gets interesting.
Even though Mahayana's attempts to interpret Buddha's Nobel silence clarified the first dangerous consequence of misunderstanding Buddha's teaching it unfortunately just intensified the second dangerous consequence of misunderstanding Buddha's teachings. Buddha's teachings of Anatta (no-self) sounded dangerously close to Nihilism (nihilists claim human life is essentially meaningless). Mahayana school's emphasis on the broader emptiness/Nothingness of the world in addition to Anatta(no-self) made the claims Buddhism is nihilistic even more credible. Buddha and Buddhist philosophers after him established what we perceive as reality is an illusion with formidable logic. So when they refuse to positively assert what happens when we wake up from this illusion, Buddhism ended up presenting a very grim and depressive conclusion to the masses.
So there was on the one end, traditional Hindu philosophies which have optimistic conceptions of what happens after enlightenment but they couldn't logically refute Buddhist philosophies. On the other end, Buddhist philosophies seem to possess irrefutable proof on their side but seem to have a pessimistic conception of what's after enlightenment. So when the hero of our story Shakhara comes into the picture this was the condition of Indian philosophy. Shankara's Advaita philosophy with mind-blowing logic explains the true nature of reality, what is the root cause of suffering, how can you be free from suffering, what happens at the moment of enlightenment, and positively assert what is after enlightenment. That is the beauty of Advaita, it is a complete philosophy.
