The current understanding is that that brahman/paramAtma/bhagawAn is that universal, inter-galactic & inter-multiverse consciousness. But is sentience ALSO an attribute of that paramAtam/brahman/bhagawAn? sentience is awareness (consciousness + ability to perceive & feel).
"Perception" and "feeling" are functions of the mind, not Ātman. That is why the Ātman is also called "sākṣin", the witness or the observer. It is pure self-aware knowledge, nothing else.
Śvetāśvatara Upaniṣad 6.11:
एको देवः सर्वभूतेषु गूढः सर्वव्यापी सर्वभूतान्तरात्मा । कर्माध्यक्षः सर्वभूताधिवासः साक्षी चेता केवलो निर्गुणश्च ॥
The one deity, hidden within all creatures, all-pervasive, the inner Ātman of everything. The overseer of activities, the home of everything, the witness, the knower, purely without attributes.
Bṛhadāraṇyaka Upaniṣad 2.4.12:
इदं महद्भूतं अनन्तमपारं विज्ञानघन एव
This great existence, infinite and boundless, is pure consciousness only.
However, when this Ātman is conjoined with the mind and senses, that conglomerate is called the Bhoktā (the experiencer, the enjoyer, the sentient, etc.).
Katha Upaniṣad 1.3.4:
The Ātman conjoined with the mind and senses, is called the Experiencer.
So it's not the pure Ātman, but the conglomerate which we perceive as ourselves, who experience emotions, feelings, etc.
Brahman as pure consciousness is not a being in Advaita Vedanta and so cannot have feeling. Atman which is Brahman in us is also simply witness consciousness. Saguna Brahman in Advaita Vedanta or Narayana/Vishnu of Vishistadvaita/dvaita has feeling.
Consciousness is the immutable Self which is the witness-consciousness, unchanging, flawless and eternal. This witness-consciousness manifests all things, viz, the ego, the intellect, and the objects, and continues to shine even when they are non-existent. Consciousness in Advaita is often compared to a canvas on which the world-picture is painted. Just as the canvas is where the various painted figures appear, both of inanimate things like mountains and animate beings like men and animals, so also on the consciousness which is the immutable Self, the variegated world appears. Advaita is not saying that the universe is conscious.
Pancadasi of Sri Vidyaranya translated by Swami Swahananda introductory remarks
An "observer" must "observe" in some way. How does the Atman observe, if it cannot perceive in any way?
Observer does not mean just observing. When we say the observer is shiva (or athma/brahman) and the observed is shakhti (or the intelligent energy of thoughts/body/world), it means, shiva and shakhti always exist together for the perpetual duality cycles to happen. eg wake/dream, dream/deep sleep, deep sleep /turiya (samadhi or moksha), energy/matter, wave/particle, birth/death, creation/destruction, manifestation/concealment, freezing/melting, summer/winter, man/woman etc
Inanimate also has the conscious observer (shiva). But self awareness is limited to human vehicles and some animals like elephants, dolphins and some monkeys which pass the mirror test.