Ttdfjt

In Gita, Sri Krishna says:

4.6 Though I am birthless, undecaying by nature, and the Lord of beings, (still) by subjugating My Prakriti, I take birth by means of My own Maya.

4.9 He who thus knows truly the divine birth and actions of Mine does not get birth after casting off the body. He attains Me, O Arjuna.

7.24 The unintelligent, unaware of My supreme state which is immutable and unsurpassable, think of Me as the unmanifest that has become manifest.

We have also to remember that

2.28 O descendant of Bharata, all beings remain unmanifest in the beginning;; they become manifest in the middle. After death they certainly become unmanifest. What lamentation can there be with regard to them?

So Sri Krishna makes it clear that He is different from 'Unmanisfest' becoming 'Manifest' as are ALL the persons.

Given the above, does any of our scriptures allow to brand Sri Krishna as a 'Person' ('Vyakti') with 'Personality'?

The meanings of the word 'Person' according to the the Oxford Dictionary are :

1A human being regarded as an individual.

•‘the porter was the last person to see her prior to her disappearance’
‘she is a person of astonishing energy’
More example sentencesSynonyms
1.1 (in legal or formal contexts) an unspecified individual.
‘each of the persons using unlawful violence is guilty of riot’
‘the entrance fee is £2.00 per person’
More example sentences
1.2with modifier An individual characterized by a preference or liking for a specified thing.
‘she's not a cat person’
More example sentencesSynonyms
1.3 A character in a play or story.
‘his previous roles in the person of a fallible cop’
Synonyms
1.4 An individual's body.
¤‘I would have publicity photographs on my person at all times’
More example sentencesSynonyms

2Grammar
《A category used in the classification of pronouns, possessive determiners, and verb forms, according to whether they indicate the speaker (first person), the addressee (second person), or a third party (third person).

《Example sentences
《3Christian Theology
《Each of the three modes of being of God, namely the Father, the Son, or the Holy Ghost, who together constitute the Trinity.

NO ISKCON TRANSLATIONS PLEASE. And the Christan Theology meaning of course in not applicable in this case.

Can Sri Krishna be called 'a person'?

Yes, here is what Ramanujacharya says in the introduction to his Bhagavad Gita Bhashya:

Nārāyaṇa is the Consort of Sri, He is absolutely auspicious and is the
antithesis of all that is evil. His essential nature consists of Being
(sat), Consciousness (cit) and Bliss (ānanda) and these
characteristics distinguish Him from all other beings. He is veritably
a great ocean of innumerable auspicious attributes which are intrinsic
to His nature and cannot be surpassed — some of them being;
omniscience, omnipotence, sovereignty, energy, creative potency and
glory.

Nārāyaṇa has a divine form, which is both pleasing and appropriate.
His form is inconceivable, indescribable, divine, eternal and
immaculate. He is a repository of limitless perfections such as
radiance, beauty, fragrance, tenderness, pervading sweetness and
youthfulness. The Lord is adorned with suitable divine ornaments which
are diverse, infinite, amazing, eternal, flawless, unlimited and holy.

And here is what Ramanujacharya says about Narayana's incarnation as Krishna:

Under the pretext of relieving the earth of its burdens, but really in order to make Himself available
for us (frail humans) to take refuge in Him, the Lord incarnated on the earth as Sri Krishna. He thus
manifested Himself to all beings. He engaged in divine pastimes which captivated the minds and
hearts of all, high and low. He vanquished demoniac beings such as Pūtana, Śakaṭa, the two Arjuna
trees, Ariṣṭa, Prālambha, Dhenuka, Kaliya, Keśin, Kuvalaya-pīḍa, Cānura, Muṣṭika, Tośala and
Kaṁsa. He spread joy and beatitude over the entire world with the nectar of His glances and speech,
demonstrating His boundless compassion, friendliness and love for all.

When the internecine war between the sons of Pāṇḍu and the descendants of Kuru broke out, Kṛṣṇa,
the Supreme Being, the God of all gods, overwhelmed by His love for those devotees who had
taken refuge in Him, took upon Himself the humble role of the charioteer of Arjuna, so that He
could be seen by all the people

And also in chapter 15 called "Mystery of the Omnipresent Supreme Being", it is said in verse 4:

tataḥ padaṃ tat parimārgitavyaṃ yasmin gatā na nivartanti bhūyaḥ |
tameva cādyaṃ puruṣaṃ prapadye yataḥ pravṛttiḥ prasṛtā purāṇī

One should then seek that goal, attaining which one never returns. One should take refuge in
that Primal Person from whom this ancient process emanated.

So clearly Krishna can be called a person, and not just by followers of ISKCON.

Yes, the word puruṣa really means "a person", it's explained like that in the Monier Williams Sanskrit-English Dictionary:

[L=126439] a person , (pumān puruṣaḥ , a male person S3a1n3khGr2. Mn. ; daṇḍaḥp° , punishment personified Mn. ; esp. grammatical pers. ; with prathama , madhyama , uttama = the 3rd , 2nd , 1st pers. Nir. Pa1n2. ), an officer , functionary , attendant , servant Mn. MBh. &c (cf. tat-p°)

And Lord Krishna says in the Bhagavad-gita 15.18 (vedabase translation):

yasmāt kṣaram atīto ’ham
akṣarād api cottamaḥ
ato ’smi loke vede ca
prathitaḥ puruṣottamaḥ

yasmāt — because; kṣaram — to the fallible; atītaḥ — transcendental; aham — I am; akṣarāt — beyond the infallible; api — also; ca — and; uttamaḥ — the best; ataḥ — therefore; asmi — I am; loke — in the world; vede — in the Vedic literature; ca — and; prathitaḥ — celebrated; puruṣa-uttamaḥ — as the Supreme Personality.

Because I am transcendental, beyond both the fallible and the infallible, and because I am the greatest, I am celebrated both in the world and in the Vedas as that Supreme Person.

And in the following verse 19 that is repeated and there it is said that one who knows Lord Krishna as the Supreme Person without doubting, is the knower of everything, and he therefore engages himself in full devotional service to Lord Krishna.

This is how Krishnaprem, (https://en.m.wikipedia.org/wiki/Krishna_Prem), the renowned siddha Gaudiya Vaishnava saint sees the topic.He clearly answers in the negative and writes

Nor Krishna is man at all, but a great Power which, by its presence, though unknown, unseen, lightens the bitter sorrows of the world.

The sanskritdictionary.com gives the relevant meanings of 'Purusha' as

The soul; द्वाविमौ पुरुषौ लोके क्षरश्चाक्षर एव च Bg.15.16 &c. -7 The Supreme Being, God (soul of the universe); पुरातनं त्वां पुरुषं पुराविदः (विदुः) Śi.1.33; R.13.6.

It is obvious that here 'Purusha' can NOT mean person ('Vyakti') -- because three types of 'Purusha' are mentioned in the chapter 15 of the Gita: kshara, Akshara and Purusha-Uttama. If all three are translated as persons, that would be the most misleading!

in His 'The Yoga of the Bhagavad-Gita'. First Sri Krishnaprem clarifies:

To anyone who has eyes to see, Gita is based on direct knowledge of Reality, and the Path that leads to that Reality..Those eternal realities are the same now as they were thousand of years ago, and the text of Gita should be interpreted in words that refer to these realities here and now.

He explains the verse that contains the word 'Purusha' in chapter 15, sloka 4 of the Gita as

Detaching himself from  the union with the objects of both outer and inner senses, detaching himself in fact from all from whatsoever, the disciple must soar upon the trackless path of light towards the Primal Consciousness from which ages past the Cosmic Energied steamed forth. (verse 4).That Consciousness however being Absolute, is far beyond all that we know as such.Knower and Known exist in one as it is, in another way, they are not one in absolute matter.It is in fact no consciousness for us, being beyond the Fire of manifested life, the Moon of Mula-prakriti, the Sun of the unmanifested Atman.It is the Void; It is also the Full.Having gone thither, none can return again.That, Krishna says, is His Supreme Abode.That is the Goal; That is final bliss.

Krushnaprem is a foremost intellectual, a greatest Siddha Vaishnava and a top-class writer. So I lay most importance to His translation and interpretation.Those who know a minimum of both Sanskrit and English will understand that the word 'Purusha' can never be satisfactorily translated as 'Person', because The one Who lying in the 'Pura' is 'Purusha'.
Sri Krishnprem translates 'Purusha' as 'The Spirit or Consciousness'.
The entire book is available for download online in pdf format. https://www.auro-ebooks.com/the-yoga-of-the-bhagavat-gita/

The translations like 'Person' or 'The Supreme Personality of Godhead' are very very close to the Christan Theological meaning and the farthest from what the Gita and the Acharyas try to imply.

No. Krishna is the Supreme transcendental Person. We call Him satachidanand but when the devotees call Him Chidanand the "sat" is already understood. When the devotees call Him Anand or Parmanand that is He Himself, the Supreme transcendental Person. So, Anand (i.e. Bliss) is not His Name but He Himself, Chit (i.e supreme consciousness) and Sat (the supreme eternity) are His attributes here.

The devotees at same state of knowledge only try to find something which is known or unknown to them. How can a dictionary help find eternal meaning of/about God. In the B.Gita 10/10 He says, "tesham satat yuktanam bhajtam preetipurvkam, dadami buddhi-yogam tam yen mamupayantite."

We need to be in the association with the practicing devotees to get a fraction of the eternal induction (intelligence) and the real meaning of this nutshell verse.

By the way, we can only become blissful ("anandi bhavti...") and not the Bliss or "Anand" even if we get blessed with our supreme destination in devotion, i.e. Unlimited Permanent Bliss.

Everyone who wants to be blissful is searching for the same Bliss, "..anando brahamaneti vyajanaat..", but the dictionaries never reveal the eternal meaning and grammar books only tell linguistic accuracy in the literature. Here this Permanent Bliss should not be confused with the dictionary meaning of temporary fraction of the limited material bliss that animals get in eating, mating and sleeping etc.

When the devotees call Him the Person, His Supremacy and Transcendence is well understood by the scripture. Valamiki called Him "MARA" but He appeared as RAMA, the Purushotam because of his association with one of the greatest among the devotees, Lord Narada.

Sril Adi Shankracharya has very rightly said to a Pundit of Sanskrit Grammar in Varanasi, "Bhaj Govinadam, Bhaj Govindam, Govindam bhaj moddhamatte.." he was trying to find the literal meaning of the vedic literature in grammar books.