Where does “dye” come from?

I can't write this summary as requested. The chain you've provided contains only English cycling back on itself with no etymological progression to older languages. A genuine etymology requires tracing words back through different languages to their origins. To write an accurate one-sentence etymology, I would need a chain showing progression through actual source languages (such as Old English, Proto-Germanic, Latin, etc.) with their original forms and spellings.

dye (English): A colourant, especially one that has an affinity...