B.G 8.04

अधिभूतं क्षरो भावः पुरुषश्चाधिदैवतम्। अधियज्ञोऽहमेवात्र देहे देहभृतां वर ॥४॥

adhibhūtaṁ kṣaro bhāvaḥ puruṣaścādhidaivatam। adhiyajño'hamevātra dehe dehabhr̥tāṁ vara ॥4॥

The perishable state (kṣaraḥ bhāvaḥ) is called adhibhūta (that which is meant for the use of living beings). The universal being (puruṣaḥ) is referred to as adhidaivata (the divine principle). I alone am adhiyajña (the principle of sacrifice) here in the body, O best of the embodied beings.

Gīta Tātparya 8.04

In the current context, the word avyakta i.e. unmanifest, akshara i.e. imperishable, Adhiyajña i.e. essence of all sacrifices, and Adhyātma i.e. cause of all, refer to Lord Vishnu alone. The living beings are called Adhibhūta i.e. those associated with insentient.

The attainment of Brahman is the objective of the current context, after the previously given explanation. Because of the qualifier 'Tat' (that), it is indicated that Brahman is the distinct and higher principle compared to other deities like Prakṛti, etc. The reference above to 'Sādhi-Yajñaṁ ca', i.e. 'the essence of all sacrifices' (7-30), suggests the inclusion of Adhibhūta and others, creating doubt that Viṣṇu-knowledge may be something distinct. The inquiry 'What is that Brahman?' arises due to this doubt. Since lord Viṣṇu is well known as the Supreme Imperishable, the resolution is accordingly stated. To instruct even the ignorant, the resolution is given in this manner.

The doubt that 'I' (Viṣṇu) was not mentioned again is addressed by the statement 'The unmanifest assumes a manifest form,' where the term 'Avyakta' (Unmanifest) is indeed applied to Viṣṇu. The term 'Avyakta' is explained as 'The unmanifest (avyakta) is only the imperishable (akṣara)', thereby resolving the doubt.

In the statement 'Those who worship the imperishable and the unmanifest,' because of the separate questions, the distinction in the fruits for the two types of worshippers is made. The declaration 'The immutable one is called the imperishable,' and the statement 'I (Viṣṇu) am superior even to the imperishable', - it is concluded that Viṣṇu is indeed distinct (and supreme).

By stating 'I alone am Adhiyajña', it is indicated that He is the essence of all sacrifices and the perceived distinction is resolved. The inclusion is appropriate, considering His various forms only are present in the bodies of all living beings.

"Viṣṇu, who resides in the bodies of living beings, is declared to be Adhiyajña (the presiding deity of sacrifice). He alone is proclaimed as Brahman due to His all-pervading nature. Due to being the superior object of worship, being exalted, and as the cause of all, He is known as Adhyātma. The creation of beings possessing inert nature is remembered as the action of Hari (Viṣṇu). Because of His superiority over the elements, living beings are called Adhibhūta. Viṣṇu alone is the supreme divinity, and Lakṣmī is His consort. The supreme being, known as the deity presiding over Prāṇa (life force), should be known as such by men."

-stated thus in Tatvaviveka.

The question regarding the nature of Adhiyajña and its characteristics is indeed resolved by the statement 'I alone (am Adhiyajña)'.