I hate to point this out… but Tyrian purple, the real Phoenician and Roman and Byzantine royal “born to the purple” purple… is a special shade of red. It’s not our “purple” at all.
Meanwhile, the Biblical scarlet embraces all sorts of reds, from deep red and Tyrian purple, and perhaps all the way out to orange.
So yes, the Holy Spirit is saying exactly what color the robe was.
One writer says “scarlet” because he’s referencing Scripture as to the Messiah’s robe being dyed scarlet with blood, being scarlet with the winepress and the blood of the grape, and “coming with dyed garments from Bosra.” (And also as a military leader.)
The other writer says “purple” because he’s referencing the Messiah as king and wealthy man of power, wearing clothes of the most precious and expensive color in the Greco-Roman world.
Both writers are absolutely correct and accurate, and they cross-reference each other.
Both writers show the soldiers’ mockery of Jesus’ poverty and powerlessness functioning as inadvertent prophecy and praise, just as the high priests and the Sanhedrin had become inadvertent prophets at Jesus’ trial.