a costly reddish-purple dye taken from sea snails, and the wool or cloth colored with it
Argaman does not name an abstract shade the way a paint chip does. It names a specific luxury product: wool or cloth dyed with a deep reddish-purple pigment squeezed, drop by drop, from certain Mediterranean sea snails. Producing even a small amount of dye took thousands of snails, which is why finished purple cloth could cost more than its own weight in gold, and why in the ancient world only kings, priests, and the very rich normally wore it.
The word itself seems to have traveled a long road before it reached Hebrew. Its most distant root is an old Hittite and Luwian word for tribute, the payment a lesser king owed to a more powerful one, because dyed purple wool was exactly the kind of prestige gift that vassal rulers sent to their overlords in the Late Bronze Age. By the time the word reached Ugarit and the wider Levant, it had come to mean the dyed wool itself rather than tribute in general, and that is the sense Hebrew inherited.
That background explains why the word keeps turning up in the same handful of settings in the Bible. It is woven into the inner curtains of the tabernacle and the high priest's garments, marking off the most sacred space and the man who alone entered it. It clothes kings and the wealthy: Gideon strips it from defeated Midianite kings, Mordecai is dressed in it after his promotion, and the Persian palace, Solomon's furnishings, and a capable wife in Proverbs are all pictured wearing or using it. It is also a major Phoenician trade good, one of the products that made the seaport of Tyre rich. And because it was so recognizably the fabric of temple and throne, a prophet like Jeremiah can point at the very same costly cloth draped over a lifeless idol to mock the idol as a fraud dressed up in borrowed glory.
Only once, in the Song of Songs, is the word stretched into a figure of speech, comparing the rich, dark sheen of a woman's hair to this famous purple. Even there the comparison trades on the fabric's reputation for splendor and rarity, not on a plain color chart.