This is a very good observation.
We do not get much context from the other texts of the NT, since the word paidarion was only used in John 6:9. I checked the Septuagint, and it usually replaces the Hebrew word naar. Which already proves that John was using it purposefully.
https://lexicon.katabiblon.com/index.php?lemma=%CF%80%CE%B1%CE%B9%CE%B4%E1%BD%B1%CF%81%CE%B9%CE%BF%CE%BD
The Hebrew word is not very specific when it comes to the age of the person described as a naar. It can be a boy or a youth. But it also described a young man fit for the war, which would make him +20 years old (Genesis 14:24):
I will take nothing except what the young men have eaten, and the
share of the men who went with me, Aner, Eshcol, and Mamre; let them
take their share.
The word naar appears in many stories of the OT, foreshadowing the Christ himself.
Isaac is called a naar in Genesis 22. Once by Abraham and once by the angel of the LORD. Since the exact age of Isaac during the akedah is unknown and has been strongly debated, let's look at other examples.
Joseph is called a naar on many occasions. Even just before his release from prison, when he was thirty years old (Genesis 41:12):
Now a young Hebrew was there with us, a servant of the captain of the
guard. We told him our dreams, and he interpreted them for us, giving
each man the interpretation of his dream.
The rebellious Absalom was called a naar by David just before his downfall (2 Samuel 18:5):
The king commanded Joab, Abishai and Ittai, “Be gentle with the young
man Absalom for my sake.” And all the troops heard the king giving
orders concerning Absalom to each of the commanders.
A type of Messiah that was released from the pit to be exalted. An antitype of the Messiah whose death on a tree reunited the nation and returned the throne to his father. Both were in their early thirties.
On top of that, the secondary meaning of paidarion in Greek is young slave. And this is another motive linked to the person of the Messiah. Jesus was the servant of God. It is no coincidence that the law for the servant, who loves his master and wants to stay with his master forever, follows the ten commandments. Jesus is the pierced one that stays in the house of the Father forever.
In conclusion, John uses the paidarion purposefully, and with just one word, he hyperlinks the symbolical story of multiplying the bread with so many more christological texts in the OT. Additionally, the mention of barley, is just another rabbit hole that the apostle gives us to explore.