What cannot be seen is not necessarily nonexistent.
The soul is said to be non-manifest, transcending thought, and immutable. Non-manifest means that it does not appear as an object to the senses such as the eyes. Also, it cannot be completely grasped by thought, unlike ordinary objects that are dealt with by the mind or intellect.
It is not that it does not exist because we cannot see it, but rather that it exists beyond the range of our senses and normal thought. Furthermore, the soul is not something that changes shape or state like an object. If you understand its nature as being unmanifest in sensations, incomprehensible through thought, and unchanging, then you should not limit yourself to lamenting from the perspective that the soul disappears.
Japanese Translation from the Gita Press Edition - Chapter 2, Section 25: "The soul is non-manifest, beyond thought, and immutable."
Sanskrit original text
अव्यक्तोऽयमचिन्त्योऽयमविकार्योऽयमुच्यते ।
तस्मादेवं विदित्वैनं नानुशोचितुमर्हसि ॥ २५ ॥Romanization
avyakto 'yam acintyo 'yam avikāryo 'yam ucyate |
tasmād evaṃ viditvainaṃ nānuśocitum arhasi || 25 ||This soul is said to be non-manifest, beyond understanding, and immutable. Therefore, if you know it as such a thing, you should not grieve. (25)
The soul cannot be recognized by any sensation. Therefore, it is called "non-manifest." Also, it cannot be conceived of by the mind. Therefore, it is something that transcends understanding.
Furthermore, by stating that it is "immutable," the distinction between the soul (Atman) and Prakriti is emphasized. The intention is to indicate that all sensations and the mind are products of Prakriti's evolution. Therefore, they cannot comprehend their own cause, which is Prakriti.
Therefore, just like the soul, Prakriti is also non-manifest and transcends thought.
However, Prakriti is not immutable; it is subject to change. On the other hand, the soul does not undergo any changes under any circumstances.
In this way, the soul is completely different from Prakriti.
As mentioned above, if the soul is understood to be eternal, omnipresent, immutable, permanent, non-manifest, beyond comprehension, and unchanging, then it is entirely inappropriate and unreasonable to grieve about it.