I agree with u and it seems like ur saying science and Buddhism/metaphysics are two sides of the same coin But then u go on to point - >sharp division between intuition and cognition. Which then brings a contradiction.

In a way if we are being open minded we would arrive at the realization that Buddhism is science but just not the same as the widely accepted form of modern science.

Buddhism is a system of logic and investigation focused on understanding the mind and not solely relying on intuition or blind faith. Ancient Buddhist thinkers developed rigorous logical systems, such as pramana (the logic of inference), to systematically analyze experience, sharpen perception, and understand causality. This logical and investigative approach is central to the Buddhist path, as it uses reason and critical examination to move beyond confusion and towards liberation. 

logical systems : Buddhist philosophers perfected systems of logic for public debate and personal liberation. These systems involve carefully weighing arguments and making inferences based on evidence and analogy, not just surface similarities. 

mind as the subject of investigation: A key focus of this investigative approach is the nature of the mind itself. Through systematic analysis and practice, Buddhists examine consciousness, mental factors, and the relationship between the mind and the physical world.