Therefore we should take Bhagavad-gītā as it is directed by the Personality of Godhead Himself.

(Introduction
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Bhagavad Gita As It Is Macmillan Edition)

The Lord Himself also establishes Himself as the Supreme Personality of Godhead in the Bhagavad-gītā, and He is accepted as such in the Brahma-saṁhitā and all the Purāṇas, especially the Śrīmad-Bhāgavatam, known as the Bhāgavata Purāṇa (Kṛṣṇas tu bhagavān svayam).

confirmed by all great ācāryas (spiritual masters) like Śaṅkarācārya, Rāmānujācārya, Madhvācārya, Nimbārka Svāmī, Śrī Caitanya Mahāprabhu and many other authorities of Vedic knowledge in India.

Of course the word "bhagavān" sometimes refers to any powerful person or any powerful demigod, and certainly here Bhagavān designates Lord Śrī Kṛṣṇa as a great personality, but at the same time we should know that Lord Śrī Kṛṣṇa is the Supreme Personality of Godhead, as is

The speaker of Bhagavad-gītā is Lord Śrī Kṛṣṇa. He is mentioned on every page of Bhagavad-gītā as the Supreme Personality of Godhead, Bhagavān.

We cannot take the medicine according to our own whim or the direction of a friend.

It must be taken according to the directions on the label or the directions given by a physician. Similarly, Bhagavad-gītā should be taken or accepted as it is directed by the speaker himself.

They are seeking peace in different ways,
but they can achieve real happiness only if they consult Kṛṣṇa, or the Bhagavad-gītā and Śrīmad-Bhāgavatam—

which constitute the science of Kṛṣṇa—or the bona fide representative of Kṛṣṇa, the man in Kṛṣṇa consciousness.

~Bhagavad Gita As It Is 2.8 Purport

In many parts of the world there are states which are replete with all facilities of life,

which are full of wealth, and economically developed, yet the problems of material existence are still present.