So, my question is, here Krishna is to be taken as the adjective which means - "The most attractive one / the one who's all attractive / the one who's of dark complexion".
Or it is to be taken in the proper noun form, i.e., the incarnation of the Lord - "Shri Krishna"?
It appears most translators of Rāmāyaṇa consider kṛṣṇa to be a proper noun i.e., Kṛṣṇa, the avatāra of Viṣṇu, given the context, whereas the traditional commentators treat it as an adjective mainly to resolve the contradiction that how could the author of Rāmāyaṇa or the assembled devas have known about a future incarnation of Viṣṇu.
Here's how Robert P. Goldman et al., translate those verses:
Sarga 105
1–3. Then King Kubera Vaiśravaṇa; Yama, dragger of his foes; great Indra of the thousand eyes; Varuṇa, scorcher of his foes; the great god, majestic Śiva, with his half-six eyes and the bull on his banner; and Brahmā, foremost of those who know the vedas, the creator of the entire universe—all these assembled in their flying chariots as radiant as the sun, and, coming to the city of Laṅkā, they approached Rāghava.
Then, raising their broad arms covered with bracelets, the foremost of the thirty gods addressed Rāghava, who stood before them, his hands cupped in reverence.
"How can you, the creator of the entire universe, the most ancient one, and foremost among those possessing supreme knowledge, stand by and watch as Sītā falls into the fire, eater of oblations? How can you not realize that you are the foremost among the hosts of the gods?"
...
"You are the imperishable Brahman, existent in the beginning, the middle, and the end. You are the highest governing principal of all the worlds, the four-armed Viṣvaksena."
"You are the wielder of the horn bow, you are Hṛṣikeśa, the primal person, the Supreme Spirit. You are Viṣṇu, the invincible wielder of the sword, and you are Kṛṣṇa of immense strength."
"You are the leader of the hosts. You are the leader of all beings. You are intelligence, strength, forbearance, and self-control. You are the origin and the dissolution. You are Upendra, Indra's younger brother, and Madhusūdana, slayer of the asura Madhu."
...
"Your body is this world; your steadfastness, the earth. Agni is your wrath; Soma, your gentleness, O bearer of the Śrīvatsa mark."
"In ancient times, you spanned the three worlds with as many strides. After confining the great asura Bali, you made great Indra king."
"Sītā is Lakṣmī; you are the god Viṣṇu. You are Kṛṣṇa. You are Prajāpati, the lord of creatures. It was in order to slay Rāvaṇa that you entered a human body here."
"Thus have you accomplished our purpose, foremost of upholders of righteousness. Rāvaṇa has been slain. Now, Rāma, in your delight, please return to heaven."
...
NOTES:
14. ... "and you are Kṛṣṇa of immense strength" kṛṣṇaś caiva bṛhadbalaḥ: Roussel (1903, vol. 3, p. 389) and Pagani (1999, p. 1187) understand bṛhadbalaḥ as a separate proper name. Dutt (1893, p. 1511) and Shastri (1959, vol. 3, p. 339) render it separately as an adjective. Raghunathan (1982, vol. 3, p. 340) and Gita Press (1969, vol. 3, p. 1855) appear to translate as we do. Most commentators understand the term bṛhadbalaḥ, "of immense strength," to refer to the Lord's great power to sustain or uphold (dharaṇasāmarthyam—so Cg). Ct and Ck take it to mean that he has the ability to hold up the entire universe as if it were a ball to play with (aśeṣabrahmaṇdasya līlākandukavaddhāraṇakṣamaḥ—so Ct). Cm, however, takes the epithet to be to the Rāmāvatāra, understanding bala in its sense of "army," and glossing, "he who has great armies of monkeys (bṛhanti vānarabalāni yasyeti tathā)." On the name Kṛṣṇa, see note to verse 25 below.
...
25. "You are Kṛṣṇa" kṛṣṇah: Literally, "Kṛṣṇa." The commentators generally agree that this term should be taken in its adjectival sense of "black, blue-black, or of a dark color (kṛṣṇavarṇaḥ)." This is probably because they wish to avoid the apparent anachronism of mentioning an avatāra who will not appear until the next cosmic age. Nonetheless, in the context of this thoroughgoing Vaiṣṇava stotra, like all translators consulted, with the exception of Raghunathan, we believe that the reference is probably to the name of the other major avatāra of Viṣṇu. Raghunathan (1982, vol. 3, p. 341), reading the adjective with devaḥ, "the god," renders, "the Lord that has assumed a dark form." See note to verse 14 above.
"You are Prajāpati, the lord of creatures." prajāpatiḥ: Literally, "Prajāpati." The epithet is most frequently used of the speaker, Brahmā himself. See note to verse 6 above.
