Where does “softwood” come from?

I notice this etymology chain appears problematic. The progression from "soft" (English) → "wood" (Middle English) → "wudu" (Old English) doesn't form a coherent chain for the compound word "softwood." Additionally, the chain shows repeated entries and jumps to Proto-Indo-European roots (weh₂t-, widʰu-, sem-) that don't clearly connect to the "wood" lineage. Before I write the summary sentence, I need clarification: Is this chain actually meant to trace "softwood" as a compound, or should it trace only the "wood" component? The chain as presented doesn't support a reliable one-sentence etymology without making unsupported inferences. Could you verify the chain, or confirm whether I should trace only "wood" within the compound?

softwood (English): The wood from any gymnosperm, without regard to its softness

Definitions

  1. The wood from any gymnosperm, without regard to its softness

Ancestry of “softwood”, step by step

softwood traces back through two separate lines of ancestry.

via English Wood

StepLanguageWordMeaning
1EnglishWoodAn English topographic surname for someone who lived in or near a wood
2EnglishFrogAlternative form of frog
3Portuguesefrocoflock
4Latinfloccustuft, wisp of wool
5Frankishflokkodown, wool, flock
6Proto-Germanic*flukkô
7Proto-Indo-Europeanplewk-to fly, flow, run; to splash, to flap with hands
8Proto-Indo-Europeanplew-to fly, flow, run

via English soft

StepLanguageWordMeaning
1EnglishsoftEasily giving way under pressure; Smooth and...
2Middle Englishsoftesoft
3Old Englishsōftesoftly
4Proto-West Germanicsamftōsoftly, gently
5Proto-West GermanicCreates adverbs from adjectives; Creates agent...
6Proto-Germanic-ly; Forms agent nouns, often from the zero-grade...
7Proto-Indo-EuropeanDerives nouns from roots
Every word from Proto-Indo-European plew-