Omniscient is a property of Ishwara i.e. Saguna Brahman not Nirguna Brahman.
As per Gita Krishna alone is omniscient.
O Arjuna, as the Supreme Personality of Godhead, I know everything that has happened in the past, all that is happening in the present, and all things that are yet to come. I also know all living entities; but Me no one knows.
Nirguna Brahman in Advaita which is said to be the higher Brahman in Advaita is a state of being which is devoid of sorrow. In Mandukya Up we find the below verse, this points to some form of sentience (note that the verse says its beyond sentience and lack of it) but certainly not omniscience
The fourth aspect of Atman or Self is Turiya, literally the fourth. In this fourth state, consciousness is neither turned outward nor inward. Nor is it both outward and inward; it is beyond both cognition and the absence of cognition. This fourth state of Turiya cannot be experienced through the senses or known by comparison, deductive reasoning or inference; it is indescribable, incomprehensible, and unthinkable with the mind. It is serene, auspicious, and non-dual.
The Nirguna Brahman is just the pure jivatma without any covering of mind and matter. So Advaita teaches the jivatma itself as the highest goal i.e. jivo brahmaiva na parah. It is also similar to purusha element in sankhya.