I'm aware of this meaning but I've never used it and I'm fairly sure I've never heard other natives use it either. I'm British. I have a feeling it's old-fashioned. Or it might still exist in other dialects.

Hi Oscar Both of them are correct (exactly and completely) But don't forget this word is informal

Those are natural for North American English, but dated. I haven’t heard them since my youth.

'Plumb' is used to convey something is perpendicular rather than 'exact' or 'complete'. Your second example doesn't make sense. You probably mean 'I plain forgot our date'.

'Plumb' means absolutely correct. We often say 'spot on' for this.