[Mark 6:3 (and Matthew 13:55-56) use the terms **adelphos
and
adelphai. biblehub.com/interlinear/mark/6-3.htm
These are defined brother and sister.
biblehub.com/strongs/greek/80.htm biblehub.com/strongs/greek/79.htm
These words are used many times in the New Testament to mean biological sibling or brother/sister in Christ. These 2 terms are never used to describe an extended family member or kinsman.
biblehub.com/greek/strongs_80.htm biblehub.com/greek/strongs_79.htm
So the words in the 1st-century inspired Greek texts used to mention Jesus’ brothers and sisters in Mark 6:3 and Matthew 13:55-56 were exclusively used to refer to brother and sister.
In Acts 2:29, Peter addressing the crowd of Jews in Jerusalem, saying, “Brethren (
adelphos), I may say to you confidently of the patriarch David that he both died and was buried, and his tomb is with us to this day.”
In response to Peter’s speech, the crowd of Jews said to the Peter and the rest of the Apostles, "Brethren (
adelphos), what shall we do?” (Acts 2:37)
In Acts 3:12,17, Peter addressing the people at Solomon’s Portico, said, "Men of Israel, … brethren (
adelphos), I know that you acted in ignorance, as did also your rulers.
In Acts 7:2, Stephen addressed the Jewish Council in Jerusalem, saying, “Brethren (
adelphos) and fathers, hear me.”
Later in his speech, in Acts 7:23, Stephen said of Moses, “When he was forty years old, it came into his heart to visit his brethren (
adelphos), the sons of Israel. 24 And seeing one of them being wronged, he defended the oppressed man and avenged him by striking the Egyptian. 25 He supposed that his brethren (
adelphos) understood that God was giving them deliverance by his hand, but they did not understand. 26 And on the following day he appeared to them as they were quarreling and would have reconciled them, saying, ‘Men, you are brethren (
adelphos), why do you wrong each other?’”
Barnabas and Paul went into the synagogue at Antioch of Pisidia and "after the reading of the law and the prophets, the rulers of the synagogue sent to them, saying, “Brethren (
adelphos), if you have any word of exhortation for the people, say it.” So Paul stood up, and motioning with his hand said, 'Men of Israel, and you that fear God, listen . . . Brethren (
adelphos), sons of the family of Abraham, and those among you that fear God, to us has been sent the message of this salvation . . . Let it be known to you therefore, brethren (
adelphos), that through this man forgiveness of sins is proclaimed to you, (Acts 13:15-16,26,38)
When Paul was arrested at the Temple in Jerusalem he addressed the people, saying, “Brethren (
adelphos) and fathers, hear the defense which I now make before you.” (Acts 22:1)
I’m not an expert in Greek but the above examples from the New Testament seem to show that the word “brethren” (
adelphos) had a much broader usage at the time than you suppose and seems to have been used to mean anything from “full brother” to the much more general “fellow Jew” or, as you pointed out in the case of Christians, “fellow Christian.”