Did shankara have a major impact in the Astika-buddhist philosophical fight?
He might have helped v1s with buddhist leanings remain vaidika-friendly, due to his acceptance of vivartavAda. But consider the more common claim that he actually defeated buddhus and turned them into vaidikas.
There is no contemporary evidence of this happening.
Even his “defeat” of maNDana-mishra is mythical (as admitted by kuppusvAmi shAstri himself, as reported by subrahmaNya shAstri in ब्रह्म-सिद्धि intro).
So, let us look at other similar cases.
Whatever is “cool”, some people try to find them in “vedas” etc. -
Similarly, it is not impossible that S and his predecessor gauDapAda (who explicitly, comically, needed to clarify - “तथा ज्ञानं नैतद्बुद्धेन भाषितम् ॥ ४.९९ ॥” in his kArika extension) tried to do the same with the vivarta-vAda of mAdhyamika bauddha provenance.
Does such an attempt succeed in bringing contrarians into the orthodox fold?
So, was S’s attempt successful like the latter?
Historically, we find buddhism continuing with strength in their centers such as nalanda. If anything, tAntrism (of Astika origin) may have subverted them - but they’d “domesticated” that as well. Ultimately, they were downed by the muslim invasion from afghAnistAn to bengal, despite collaborating with them against their hated “tIrthaka-s” (eg. McLean thesis on sindh here).
Contemporarily, we find the example of chinna-jIyar of telangAna/ AP foisting “social justice” (mild “wokism”) on to rAmAnuja - this was apparent in the “statue of equality” website. Some claimed that this helped bring some antagonistic people into the tradition. However, we find that people who actively engage with inimical narratives (eg. “shiva shakti” in the same AP & TE) being far more credibly successful.
Similarly, one can estimate that udayanAchArya and jayanta bhaTTa (even kumArIla the mImAMsaka?) having a far greater impact against the bauddha-s than shankara.