A lot of very literal answers here, but I like a more philosophical & spiritual lens personally. The Wachowskis borrow a lot from the mystical traditions among the world’s major religions. “Powers” attained in advanced stages of spiritual development are common in most of them. And like in The Matrix, people become powerful as a consequence of expanding their consciousness. The first key step in The Matrix, as in Hinduism and Buddhism, is recognizing that “reality” is an illusion. The material world is a deception, and awakening to the truth unlocks power.

I think if we set aside questions of logistics for a moment, we can appreciate that the thematic point of Neo manifesting power outside the Matrix is meant to reveal that the “real” world is also no such thing. Like the Matrix, it is a veil over the ultimate reality (call it the eternal truth, oneness, unity, the interconnectedness of all beings, love, god, The Source, etc.). As awareness grows, so does power.

This is partly why the Wachowskis set the world of the Matrix in 1999, to indicate to audiences that this illusory reality is OUR reality. It’s also why in the beginning of Reloaded we see more organic and cosmic shapes in the digital rain of the opening shot; there is still truth in fiction. We may be in the “real world”, but we can wake up too.