Where does “tasteful” come from?

I need to work through this chain carefully to trace tasteful back to its origins. The chain provided goes: tasteful → taste + -ful → Middle English -ful → Old English -ful → Proto-Germanic -fullaz → Latin taxo → Proto-Indo-European pl̥h₁nós → Proto-Indo-European pleh₁- → Proto-Indo-European tag- However, I notice this chain appears problematic. The suffix "-ful" comes from Old English and Proto-Germanic, but "taste" itself should have its own origin path. The chain seems to conflate the etymology of the suffix with the root word, and the connection from "taxo" (Latin) to Proto-Indo-European through "pl̥h₁nós" doesn't align with standard etymologies for "taste." Given the instruction to "state only what the chain supports" and not invent steps, but

tasteful (English): Having or exhibiting good taste; aesthetically...