How are you using the word "primary"? Do you mean "sibling" is the first definition you find in the dictionary for the word "brother" (
ἀδελφός, Adelphos)? Initially it seemed you were using it in a misleading way to downplay how common its other usage was.
Primarily means that it appeared, scripturally speaking, that adelphos as 'from the same womb' was the predominant use of the word. That is, more instances were found of it referring to children of the same parent, or parents, rather than cousins or further relations.
Regarding your request for proof the Blessed Virgin Mary was chaste all Her life, what proof would you even be willing to accept?
An explicit statement saying that 'Mary remained a virgin all her life', or, 'Mary, the perpetual virgin'. Either one would work, ...for starters. Then, you would need to explain the significance, and how such a disposition on Mary's part, after her hymen was already broken, brings glory to God and Jesus? Yes, there is merit to celibacy, but not while enjoying the presence of a husband and a family. Meaning, her devotion is already divided by her spousal or matriarchal duties.
These are explicit statements, that taken at face value, do not require further exegesis or etymologies.
John 7:3-5
7:3. Therefore
His brothers said to Him, "Leave here and go into Judea, so that Your disciples also may see Your works which You are doing. 4. "For no one does anything in secret when he himself seeks to be known publicly. If You do these things, show Yourself to the world." 5. For not even
His brothers were believing in Him.
Mark 3:20-21
3:20. Then Jesus entered a house, and again a crowd gathered, so that he and his disciples were not even able to eat. 21. When
his family heard about this, they went to take charge of him, for they said, "He is out of his mind."
Mark 6:3-4
6:3. "Where did this man get these things?" they asked. "What's this wisdom that has been given him, that he even does miracles! Isn't this the carpenter? Isn't this
Mary's son and the brother of James, Joseph, Judas and Simon? Aren't
his sisters here with us?" And they took offense at him. 4. Jesus said to them, "Only in his hometown, among his relatives
and in his own house is a prophet without honor."
The underlined expression here has no weight, if they were relatives - his point would be moot.
Mark 3:31-35
3:31. Then Jesus' mother and brothers arrived. Standing outside, they sent someone in to call him. 32. A crowd was sitting around him, and they told him, "Your mother and brothers are outside looking for you." 33. "
Who are my mother and my brothers?" he asked. 34. Then he looked at those seated in a circle around him and said, "Here are my mother and my brothers! 35. Whoever does God's will is my brother and sister and mother."
Would one mention his Mother and 'cousins' in such a context as below?
Matthew 13:54-57
13:54. Coming to his hometown, he began teaching the people in their synagogue, and they were amazed. "Where did this man get this wisdom and these miraculous powers?" they asked. 55. "Isn't this the carpenter's son? Isn't his mother's name Mary, and aren't his brothers James, Joseph, Simon and Judas? 56. Aren't all his sisters with us? Where then did this man get all these things?" 57. And they took offense at him. But Jesus said to them, "Only in his hometown and in his own house is a prophet without honor."