What does the statement "one who knows Brahman or Atman knows everything" mean? Does it mean he has all scientific and material knowledge or does it refer to spiritual knowledge?

It means he knows the essence of things. The reality behind surface phenomena. The constant unchanging principle that persists underneath the changing forms and names. The ultimate unchanging substratum upon which all the worldly phenomena occur. The silent observer, the reconciliation of all opposites. The singular point which is both the merging and emerging of opposites. Of the nature of unconditioned existence, unconditioned awareness, unconditioned bliss.

The method of science involves a Subject making empirical observations of Objects separate from the Subject via sensory perception.

The method of Ātmavidyā involves the Subject observing the Subject without sensory perception, because the nature of the Subject is inscrutable to sensory perception. But more importantly, because the nature of the Subject is closer to the Subject than any external Object.

This is termed अपरोक्षानुभूतिः (aparokṣānubhūti) — non-indirect perception. It is “indirect” because it is not through the medium of the senses. It is “non-indirect” because it is even closer and clearer than what is perceived through the medium of the senses. It is that which occurs “behind the scenes”.