How do different Buddhist traditions view scriptural authority regarding supranormal phenomena?

Buddhist scriptures describe numerous supranormal phenomena such as the existence of devas (gods), multiple cosmological realms such as heaven and hell, and the continuity of consciousness or reincarnation that are inaccessible to ordinary sensory perception and cannot be established through conventional inference. This raises a question about the nature of scriptural authority across Buddhist traditions. Do schools such as Theravāda, Mahāyāna, or Vajrayāna treat scripture or scriptural revelations as independent, authoritative proof of such phenomena, in a manner analogous to how śruti functions in Hindu Vedānta, where the text itself serves as an epistemic source? Or are these teachings primarily seen only as guiding principles for ethical conduct, meditative practice, and direct experiential verification, rather than as conclusive evidence of supranormal realities? References to classical texts, commentaries, or doctrinal discussions that clarify whether the status of scriptural proof in Buddhism is regarded as epistemically authoritative for realities beyond perception and inference would be especially illuminating.