Is it true that Buddhism declined in India due to the Advent of Advaita Vedanta of Adi shankaracharya?

It seems to be a widely held belief held by Hindu scriptures and scholars that The God Shiva incarnated as Adi Shankaracharya in order to stop buddhism. > “In this regard, it is stated in the Padma Purana that Lord Siva > appeared as a brahmana in the age of Kali to preach the Mayavada > philosophy, which is nothing but a type of Buddhist philosophy. It is > stated in Padma Purana: **Lord Siva, speaking to Parvati-devi, > foretold that he would spread the Mayavada philosophy in the guise of > a sannyasi brahmana just to eradicate Buddhist philosophy. This > sannyasi was Sripada Sankaracarya. In order to overcome the effects of > Buddhist philosophy and spread Vedanta philosophy, Sripada > Sankaracarya had to make some compromise with the Buddhist philosophy, > and as such he preached the philosophy of monism, for it was required > at that time.** Otherwise there was no need for his preaching Mayavada > philosophy. At the present moment there is no need for Mayavada > philosophy or Buddhist philosophy, and Lord Caitanya rejected both of > them. This Krishna consciousness movement is spreading the philosophy > of Lord Caitanya and rejecting the philosophy of both classes of > Mayavadi. Strictly speaking, both Buddhist philosophy and Sankara’s > philosophy are but different types of Mayavada dealing on the platform > of material existence. Neither of these philosophies has spiritual > significance. There is spiritual significance only after one accepts > the philosophy of Bhagavad-gita, which culminates in surrendering unto > the Supreme Personality of Godhead. ~ Swami Bhaktivedanta Prabhupada on Srimad Bhagavatam 4.24.17 > The exact word used in Sanskrit is nāstika, which refers to one who > does not believe in the Vedas but manufactures some concocted system > of religion. Śrī Caitanya Mahāprabhu has said that the followers of > the Buddhist system of religion are nāstikas. In order to establish > his doctrine of nonviolence, **Lord Buddha flatly refused to believe in > the Vedas, and thus, later on, Śaṅkarācārya stopped this system of > religion in India and forced it to go outside India.** ~ Swami Bhaktivedanta Prabhupada on Srimad Bhagavatam 4.2.30 ---------- Now my question is NOT about what buddhists think about the validity of Advaita or Whether Shankara was an incarnation. What I am more interested in knowing is that was it really Vedanta / Adi shankara's philosophy that was the main factor responsible for the decline of Buddhism in India? What do Buddhist experts themselves opine on the matter? ---------- Edit:- It would appear the question has been flagged as duplicate. I have seen the linked question and it does not specifically address the question since none of the answers have discussed how much role Adi shankara played in the decline of buddhism in india. I would request the question to be re-opened as I am skeptical of the notion that Adi shankara philosophically defeating buddhists was the major reason behind the decline of buddhism in India and I would like to see If any evidence can be found to the contrary.