BTW, I proposed here that the Buddha’s ascetic practices were Brahmanical — or at least some continuation of Brahmanical-like mysticism which he learned from Ālāra Kālāma and Uddaka Rāmaputta, perhaps influenced by experimental mortification practices. I think all of the circumstantial evidence and fragmentary clues point to this being the case. Snp 3.2 is a good example as well: Māra temps the Buddha to perform the agnihotra and make merit while he is doing extreme austerity, though seemingly less extreme than the earliest period.
The Buddha’s other first sermons were plays on the controlling ātman, and the burning of fire / maintaining the sacrificial fire. Extreme asceticism was a Brahmanical practice, not just a Jain one, and the breath control meditations are specifically brahmanical.
Also: I wish I had included this originally. I haven’t seen it discussed much (or ever), but at SN 35.103, the Buddha says that Uddaka Rāmaputta used to call himself a ‘vedagū’ (master of the Veda) — precisely what the Upanisads say — and a ‘sabbajī,’ which if we read in a more pregnant philosophical sense, this would be ‘sabba’ as in ‘the Whole/All,’ related to brahmán and the cosmic ātman. This doesn’t directly relate, but this is yet another time where Uddaka Rāmaputta comes up in a Brahmanical context or saying something Upanisadic.