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On the contrary in the Bible brother has shades of meaning because Aramaic and other Semitic languages do not differentiate between a blood brother/sister and a cousin or other

For example

MAtt 1:2 "Jacob the father of Judah and his brothers," for step-brothers with the same father but different mothers
acts 3:17 "17And now, brethren,"
Luke 10:29 "and who is my brother"
Matt 5:47
Matt 23:8
Rev 22:9

So, yes, brothers had a wider meaning then just blood brother. And no, the term "Irdu" is not used biblically.

The NT was written in Greek, ok -- not all, but let's take your argument for the sake of argument. Remember also that the words of Jesus were mostly Aramaic or Hebrew or maybe even GReek -- we've already shown that in SEmitic languages like Aramaic/hebrew there is no differntiating term between a blood brother and a cousin, let's examine the GReek ouch outos estin o tekton o uios Marias adelphos de Iakobou Iose kai Iouda kai Simonos

If the term is that the adelphoi have the same mother then it would be ho adelphos But that is not used. Without the article adelphos is non-specific and non-exclusive and can mean kinsmen, relatives

Furthermore, I give you two examples of why He didn't have blood brothers of the same mother

Why give John to look after Mary -- that would be quite "rude" (at the very least) to his other brothers, not something a Jew in those days would do
Why does Mary act surprised when the Angel tells her she will conceive?

He also had brothers, half brothers.

perhaps brothers from his father's earlier wife maybe, or more plausibly cousins.

Have you been to the Middle-East lately? A guy will call his cousin his brother. This is true of this clan society just as it was in the time of Christ.

More importantly, you have no proof that they were the children of Mary -- if they were, then why did Jesus tell John to take care of His mother? that's a classic affront if he had any brothers through Mary