What was the philosophical and doctrinal affiliation of Uddaka Rāmaputta?

In early Buddhist sources, Uddaka Rāmaputta is described as one of the teachers under whom Siddhartha Gautama studied before attaining enlightenment, immediately after his training with Āḷāra Kālāma. The Pāli Canon (e.g MN 26) and parallel Sanskrit sources suggest that Uddaka Rāmaputta taught a form of meditative attainment described as “āruppajhāna”, culminating in a state of “neither perception nor non-perception” (naivasaññānāsaññāyatana). Some Scholars such as Alexander Wynne have hypothesised his affilation with Upanishadic streams of thought by theorizing that Uddaka Rāmaputta’s highest meditative attainment, naivasaññānāsaññāyatana, is identical to the Upanishadic notion of turiya, as described in the Mandukya Upanishad’s “nā prajñam, nāprajñam” (vide. The origin of Buddhist meditation, Wynne 2007) > ****nāntaḥ-prajñam, **na bahiṣ prajñam, nobhayataḥ-prajñam na > prajnañā-ghanam, na prajñam, nāprajñam**; adṛṣtam, avyavahārayam, > agrāhyam, alakṣaṇam, acintyam, avyapadeśyam, ekātma-pratyaya-sāram, > prapañcopaśamam, śāntam, śivam, advaitam, caturtham manyante, sa ātmā, > sa vijñeyaḥ. || 7 ||**** > > That is known as the fourth quarter: **neither inward-turned nor > outward-turned consciousness, nor the two together; not an > indifferentiated mass of consciousness; neither knowing, nor > unknowing**; invisible, ineffable, intangible, devoid of > characteristics, inconceivable, indefinable, its sole essence being > the consciousness of its own Self; the coming to rest of all relative > existence; utterly quiet; peaceful; blissful: without a second: this > is the Ātman, the Self; this is to be realised. (7) (Mandukya Upanishad, Verse 7) While academic scholars like Wynne emphasize these philosophical affinities with Upanishadic thought, it still remains unclear how traditional Buddhist scholarship situates Uddaka. How do Pali texts and classical commentaries classify his meditative system and doctrinal orientation? Was he regarded as belonging to a specific sramanic or Brahmanical school, or is he primarily interpreted as a precursor within the Buddha’s own spiritual biography?