When Witches (fairy godmother variety) and Wizards rely on inanimate objects such as wands, staffs and plain golden rings etc it's a general 'law' in the fantasy genre that said object(s) are invested with some of the practitioner's power which, in Drum Billet's and Coin's daddy's cases, goes on after their death.
Esk and Coin's 'inheritance' of those objects does not take away from their own innate magical of ability, 'cos they didn't make their staffs so their own abilities/powers are 'pure' and not
shared with their staff - Coin as the 8th son cubed which we are told = Sourcerer. Esk's own ability is in question here as to origin
as she, not being an 8th son
of an 8th son, should not be a wizard, but she is given possession of wizard's staff nonetheless.
So a hypothesis for deliberation here. Are Witches, like Wizards, subject to the power of 8 willy nilly? We are not told this, but I suspect with Esme and Lily Weatherwax as models (one with a wand), their mother and various other magical adepts of both genders cropping up in their family tree (an Archancellor as well as Black Alice) I would say that they're almost certainly NOT subject to it at all. Concentrating on Esk, not being bound by the rule of 8 in males doesn't
rule out that she has magical ability of her own. She does not take the staff out Borrowing for instance - she does that on her own doesn't she? And the spirkles and weevils are down to magic of some kind but what 'kind' - or is there no 'kind' as such only different disciplines with fairy godmothering more akin to wizardry?
Wands/staffs on Discworld are magic enhancers or power channeling devices. However, they're possibly also a drain on the individual's own innate skills and perhaps can create too much inter-dependancy with their original owner - certainly in Drum Billet's case and I think that this explains why Esk can't really control it or direct how it's used to some extent, although it does a reasonable job of keeping her safe. I don't think the staff is Drum, just his residual power lingering in the object so it's not got a telepathic link to her except perhaps it can 'sense' when she needs to augment her own power and then, because she's female
there's a basic 'blowing of fuses' because the staff and Esk have the wrong sort of wiring to work together effectively and they only work 'properly' apart from each other - so knocking Simon out is purely down to the staff and likewise Esk going off to battle in the DD and not using magic at all, under her own steam?
Anyway - pull that apart a bit