Is everything in the universe conscious according to Hinduism?
No, not everything is conscious.
According to Viśiṣṭādvaita propounded by Sri Rāmānujāchārya, the Vedas declare that there exist 3 independent tattvas (entities), which are chit (Jivatmas), achit (matter), and Ishvara (Brahman). Ishvara, or Brahman, exists as the Antaryami (inner-self/inner-ruler) of chit and achit.
The first line of Ramanujacharya's work known as the Vedārthasangraha , or "summary of the meaning of the Vedas," says:
I offer adoration to Vishnu, the all-pervading Supreme Being, who is
the overlord of all
sentient and non-sentient entities
By "sentient" it is meant chit, and by "non-sentient" it is meant achit.
Here is a more direct explanation:
The Being [Brahman or Sat] itself, the material and efficient cause of the world,
thought, ‘Let me be many, let me multiply (Chan. 6:2:3)’........
Thus, the section of the Upanishad under consideration develops in
details the thought that the entire universe of sentient and
non-sentient entities has Being as its material cause, its efficient
cause, its ground, its controller and its Lord to which it is
instrumental in value.
However, one can say that since Brahman, who is dwelling as the Antaryami of achit, is sentient, then achit is also sentient. But achit by itself is not sentient.