How does Catholic Church view the new school of thought on multiplication of bread by Jesus?

The Catholic Church has very specific rules for the interpretation of Scripture. This view is not new, nor is it Catholic. The primary sense of Scripture is the literal sense which would require a primary reading of the multiplication of loaves and bread as actual miracles. Note the allegorical sense can also be called the typological sense, in which the OT has a type of NT character such as St. Paul calling Jesus the last Adam (1 Corinthians 15:45).

The senses of Scripture

115 According to an ancient tradition, one can distinguish between two senses of Scripture: the literal and the spiritual, the latter being subdivided into the allegorical, moral and anagogical senses. the profound concordance of the four senses guarantees all its richness to the living reading of Scripture in the Church.

116 The literal sense is the meaning conveyed by the words of Scripture and discovered by exegesis, following the rules of sound interpretation: “All other senses of Sacred Scripture are based on the literal.” [St. Thomas Aquinas, S Th I, 1, 10, ad I.]

117 The spiritual sense. Thanks to the unity of God's plan, not only the text of Scripture but also the realities and events about which it speaks can be signs.

1. the allegorical sense. We can acquire a more profound understanding of events by recognizing their significance in Christ; thus the crossing of the Red Sea is a sign or type of Christ's victory and also of Christian Baptism. [Cf. I Cor 10:2.]
2. the moral sense. the events reported in Scripture ought to lead us to act justly. As St. Paul says, they were written “for our instruction”. [I Cor 10:11; cf. Heb 3:1 - 4:11.]
3. the anagogical sense (Greek: anagoge, “leading”). We can view realities and events in terms of their eternal significance, leading us toward our true homeland: thus the Church on earth is a sign of the heavenly Jerusalem. [Cf. Rev 21:1 - 22:5.]

118 A medieval couplet summarizes the significance of the four senses: The Letter speaks of deeds; Allegory to faith; The Moral how to act; Anagogy our destiny. [Lettera gesta docet, quid credas allegoria, moralis quid agas, quo tendas anagogia.]

119 “It is the task of exegetes to work, according to these rules, towards a better understanding and explanation of the meaning of Sacred Scripture in order that their research may help the Church to form a firmer judgement. For, of course, all that has been said about the manner of interpreting Scripture is ultimately subject to the judgement of the Church which exercises the divinely conferred commission and ministry of watching over and interpreting the Word of God.” [DV 12 # 3.] But I would not believe in the Gospel, had not the authority of the Catholic Church already moved me. [St. Augustine, Contra epistolam Manichaei 5, 6: PL 42, 176.]

Catechism of the Catholic Church

Denial of miracles is one characteristic of the heresy of Modernism.

Doctors of the Church did not deny the miraculous nature of the multiplication of the loaves:

• The multiplication of the loaves was not effected by way of creation, but by an addition of extraneous matter:

  The multiplication of the loaves was not effected by way of creation, but by an addition of extraneous matter transformed into loaves; hence Augustine says on Jn 6:1-14: ‘Whence He multiplieth a few grains into harvests, thence in His hands He multiplied the five loaves’: and it is clearly by a process of transformation that grains are multiplied into harvests. (Saint Thomas Aquinas. Summa Theologica III, q. 44, a.4, ad.4)

• He who multiplied the five loaves is the same One who multiplies the fruits of the seeds:

  A great miracle: but we shall not wonder much at what was done, if we give heed to Him That did it. He multiplied the five loaves in the hands of them that brake them, who multiplieth the seeds that grow in the earth, so as that a few grains are sown, and whole barns are filled. But, because he doth this every year, no one marvels. Not the inconsiderableness of what is done, but its constancy takes away admiration of it. But when the Lord did these things, He spake to them that had understanding, not by words only, but even by the miracles themselves. (Saint Augustine. Sermon 130, no. 1)

• In multiplying the loaves, Jesus showed his power over material nature:

  But what is divine is that the five loaves were more than sufficient for five thousand people, for clearly it was not this little food that had satisfied the people, but its multiplication. As you have seen, as though by an irrepressible font abounding from the hands of the distributors the fragments that they had not yet divided, and without daring to touch them with their fingers, the pieces spontaneously appeared. When such things are read, how can we be surprised with the perpetual movement of the waters or become amazed that the liquid fonts flow without ceasing when a solid substance expands in abundance? This happens to make us see that which we ordinarily do not see. By one thing He has manifested with such evidence that he is equally the Author of the others and the Creator of all of material nature, that was not found, but made, and supplies his successive contributions to the production of all things. (Saint Ambrose. Treatise on the Gospel of Saint Luke, bk. VI, no. 84-85)

• The remains of the multiplication exceeded as fragments so that the absent might learn of the miracle:

  ‘And He brake and gave to the disciples, and the disciples to the multitude.’ The five loaves He brake and gave, and the five multiplied themselves in the hands of the disciples. And not even here doth He stay the miracle, but He made them even to exceed; to exceed, not as whole loaves, but as fragments; to signify that of those loaves these were remains, and in order that the absent might learn what had been done. (Saint John Chrysostom. Homily on Matthew, Homily XLIX)

• The fragments showed that what had taken place was no illusion:

  And I marvel not only at the quantity of loaves created, but besides the quantity, at the exactness of the surplus, that He caused the superabundance to be neither more nor less than just so much as He willed, fore-seeing how much they would consume; a thing which marked unspeakable power. The fragments then confirmed the matter, showing both these points; that what had taken place was no illusion, and that these were from the loaves by which the people had been fed. (Saint John Chrysostom. Homily on the Gospel of Saint John. Homily XLII)

source: Denzinger-Bergoglio, "Francis and the curious miracle of the non-multiplication of the loaves", which contains more magisterial teachings regarding the necessity of believing Christ's miracles