You have a point. If these 'brothers and sisters' were other than brothers and sisters and just kin of any sort, the word that would be used would most likely be syggenēs. As was used in Luke 1:36 for the relationship between Mary and Elizabeth.
syngenḗs, soong-ghen-ace'; from G4862 and G1085; a relative (by blood); by extension, a fellow countryman:—cousin, kin(-sfolk, -sman). (https://www.blueletterbible.org/lang/lexicon/lexicon.cfm?Strongs=G4773&t=KJV)
Yet in Mark 6:3, as you quoted, the relational word is adelphos which clearly indicating, at the very least, sharing one parent:
adelphós, ad-el-fos'; from G1 (as a connective particle) and δελφύς delphýs (the womb); a brother (literally or figuratively) near or remote (much like G1):—brother.
Outline of Biblical Usage: I.a brother, whether born of the same two parents or only of the same father or mother.
None of the Biblical usages indicate distant relative or closer kin (aka cousin). (https://www.blueletterbible.org/lang/lexicon/lexicon.cfm?Strongs=G80&t=KJV)
If one wanted to 'strain a gnat' the best they could come up with as an alternative translation would be national kinsmen or ancestor and brother in Christ, which does not apply to the text.
And the reason that *brother* and *sister* means actual brother and sister is precisely because they did not think Jesus was anything more than the son of the carpenter and Mary.
They had no idea who He was, didn’t believe His claims, could not even begin to figure it out. Their puzzlement was plain.
In their eyes, He was just an ordinary guy from an ordinary family. There was n o reason for them to fudge meanings.