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The "twang" or "buzzy zing" is on all frets. Not just open G (nut), not a limited portion of neck, not an individual fret.
In that case you can rule out any nut issues (at least as the source of this "buzz") + probably any issues with action and relief too.
It could still be a bad string or an issue with the G-string saddle slot, like a tiny burr that won't let the string settle properly.
If you've got a suitable file I would try a couple of GENTLE strokes in the G-string saddle slot. Just be careful that you don't widen the slot (and ideally not lower it either but this isn't critical with an adustable saddle). Also make sure you've set your witness points properly.
If that doesn't solve it, or if you don't have a suitable file, I would try a different set of strings. The stock strings could be rubbish for all I know. Maybe try a set of mellower roundwounds, like GHS Balanced Nickels?
But then again, maybe you just need to get used to roundwounds. Especially if you're playing the bass in active mode which can get pretty bright and zingy unless you're careful with the tone controls.