Before answering, anything let's just see the above premise given by the op only from Krishna Bhagwatam.
The story behind compiling SB as per SB itself is as Vedavyasa felt discontent even after compiling the Vedas, Puranas, Mahabharata and Vedanta-sutra. So he inquired Sage Narada regarding the same then Narada said that "You have not actually broadcast the sublime and spotless glories of the Personality of Godhead. That philosophy which does not satisfy the transcendental senses of the Lord is considered worthless."
So on the advice of Narada, Vyasa meditated and the Bhagavata was manifest to him.
But the premise itself is wrong. As all the 18 Maha Puranas were compiled before the Itihasa Mahabharata as mentioned in Mahabharata itself.
Mahabharata itself is the Summary of all the 18 Purānas. After completing all the 18 Purānas Vyasa composed Mahabharata which contains the summary of 18 Puranas, 4 Vedas, Upanishad, Itihāsas, etc etc.:
“Then the greatly glorious Vyasa, addressing Brahma Parameshthi, said, “O divine Brahma, by me a poem hath been composed which is greatly respected. The mystery of the Veda, and what other subjects have been explained by me; the various rituals of the Upanishads with the Angas; the compilation of the Puranas and history formed by me and named after the three divisions of time, past, present, and future; the determination of the nature of decay, fear, disease, existence, and non-existence, a description of creeds and of the various modes of life; rule for the four castes, and the import of all the Puranas”.
The Puranas can't contradict Mahabharata as all the 18 Purānas are dependent on Mahabharata as said by the sage Veda-Vyasa himself.:
“O ye Brahmana, as the four kinds of creatures (viviparous, oviparous, born of hot moisture and vegetables) are dependent on space for their existence, so the Puranas depend upon this history (Mahabharata)”.
All the 18 Puranas are equal and gives equal benifits after reading them which is same as the benifits of the devotion towards Lord Vishnu no distinction of Purānas as so called Sāttvik, Rajasik and Tāmasik gunas.:
“One devoted to Vishnu acquires (through reading this Mahabharata) that merit which is acquired by listening to the eighteen Puranas. There is no doubt in this”.
So, As SB was created after Mahabharata, which makes it as the 19th Purāna. But as there is no 19th Maha Purāna so this makes it as an Upa-Purāna.
Devi Bhagawatam 1:03:15-16.:
“Varuna Purâna. Kalika Purâna, Samva Purâna, Nandi Kes’wara Purâna, Saura Purâna, Purâna spoken by Parâs’ara, Âditya Purâna, Mahesvara Purâna, Bhâgavatam and Vasistha Purâna. These Upa Purânas are described by the Mahatmas.”
The real Bhagwata Mahapurana is as follows.:
“The Purana in which the story of the goddess Durga has been enshrined, it is called the ‘Bhagavatam’ or the ‘Devi Purana'”
Skanda Purana : Devi Bhagawata Mahatmayam : Ch1: verse 37.:
“So the Bhagawatam the Purana of Devi is superior than the supreme and greatest among the scriptures which confer dharma, artha, kama and moksha, is the opinion (of learned ones)”.
Matsya Purana 53:20-22).:
“That Purana which begins with the description of the sacred Gayatri worship, and elaborates various dharma-s, and which contains the narration of the slaying of vrittrasura, is called ‘Bhagavatam’. That Purana which narrates the stories of the great men of ‘Sarasvata kalpa’, is known as ‘Bhagavatam’. One who writes Bhagavatam and gives away in charity along with a golden Lion, on the full-moon day, in the month of ‘Bhadrapada’, attains final emancipation. This Purana contains eighteen thousand verses”.
Devi Bhagavatam 6:31:26-27.:
“Vyâsa said :– O King! Maharsi Nârada thus kindling knowledge in me, went away; I also thought over his words. On the banks of the river Sarasvatî, I composed this (Devî) Bhâgavatam to pass away my time during the excellent period of Sârasvata Kalpa.”
It's the 5th Purāna in the list and the best one.:
Devi Bhagawatam 1:1:15b-18.:
“O Saumya! (one of gentle appearance) you have recited those Purânas endowed with five characteristics and full of many narratives; of these, the fifth Purâna, equivalent to the Vedas and with all the good qualities, the Bhâgavata yields Dharma and Kâma (religion and desires), gives liberation to those who desire for emancipation and is very wonderful; you mentioned this before but ordinarily; you did not dwell on this specially. Now these Brâhmanas are eager to hear gladly this divine auspicious Bhâgavata, the best of the Purânas; so kindly describe this in detail”.
Lists of the 18 Purānas in other Purānas and SB.:
Shiva Purana 5:44:120-122.:
“Brahma, Padma, vaishnava, Shaiva, Bhagavata, Bhavishya,...
Vishnu Purana 3:06:20.:
“Those who are acquainted with the Puráńas enumerate eighteen, or the Bráhma, Pádma, Vaishńava, Śaiva, Bhágavata, and…”.
Skanda Purana: Suta Samhita 01:7-8a.:
“First is the Brahma Purana, second comes the Padma, third is the Vishnu, fourth is Shiva, after that comes Bhagavatam (fifth) thereafter comes Bhavishyat Purana”.
Brahmanda Purana.: Lalita Sahasranama: verse 226,:
“She is the fifth, the lordess of the five elements, and worshiped with methods comprising five”.
On the other hand, Krishna Bhagwatam (S.B.) placed itself as the 7th in the list.
“The eighteen major Purāṇas are the Brahma, Padma, Viṣṇu, Śiva, Linga, Garuḍa, Nārada, Bhāgavata, Agni, Skanda, Bhaviṣya, Brahma-vaivarta, Mārkaṇḍeya, Vāmana, Varāha, Matsya, Kūrma and Brahmāṇḍa Purāṇas”
Great Sage Veda Vyasa was credited to had authored Srimad Bhagavatam.
That's kind of controversial.
See this. Part 2 - The Date and Authorship of the Bhāgavata Purāṇa.
Are there any other references which indicate Bhagavata Purana is the foremost?
So, many answers are already given. At this point, I will be just repeating them so m just skipping it and moving to the next one.
The Bhagavata Purana is considered to be the purest and greatest of all the puranas.
Even if people knew that it is the foremost then why do they refer to other puranas?
It's because, Almost all the purānas say this about themselves or other purānas. See this.
Plus, Mahā Purāna >>> Upa Purāna.
Q.: If it's an Upa Purāna then why Srimad Krishna Bhagwatam is praised as the best one.?
A.: Even Upa Purānas can be considered as the best.
See this answer. Upa Purānas like Kālika Purāna prauses itself as the supreme one among the Purānas.
The transcendental pleasure and completeness which vyasadeva felt after compiling the Bhagavata Purana was not felt after compiling Vishnu,shiva,padma puranas etc. even though they describe the transcendental glories and devotion of the deity to which the purana is dedicated why is it so ?
Srimad Krishna Bhagavata Purana II.7.51-52.:
Brahma tells Narada "This brief account of the manifestation of the Lord is what is called the Bhagavata. The Supreme Being Himself gave the knowledge of it to me. I have also given to you a brief account of the Lord's glories and attributes. You elucidate it with the help of your imaginative power in a way that will generate devotion in the mind of men for Sri Hari who is the soul and support of all."
So, The Conclusion along with my Opinion.:
It's just that after compiling the hard truth about reality with politics and betrayal viz the itihāsa Mahābhārata, he was relieved hearing the glories of lord in an imaginative story way. Basically, it's same as eating sugar for sweetening the mouth after eating a bitter medicine. Plus, he should also be happy for compiling his first Upa Purāna like his father the previous Vyāsa Parāshara.
I hope this clarifies all your queries. Prd..