That example is prayer not reading, but yes there’s many Hebrew examples of meditating in the heart because most texts were memorised aurally rather than read directly.

A first century explicit example of private reading aloud is Acts 8:28–30 Philip runs up and "heard him reading" (ἤκουσεν αὐτοῦ ἀναγινώσκοντος).

Ten minutes of Claude searching the Hebrew and Greek scriptural texts came up with no examples that are explicitly private silent reading of text.