I was originally envisaging this as an effect almost so low-level as to be aesthetic, rather than an actual thing, but the more I thought about it the more I realized how incredibly useful a hand on the end of our staff would be. It would certainly be cool enough that it would be worth expending effort on it specifically, rather than asking to have it as flavor text, so that we can get it to move around at will (hopefully by thought).
I won't talk in detail about all the hand puns it would allow us to make (although it would let us make many), or how useful a grabber on a stick would be (reach it through a window and yoinketh whatever's caught our eye). Instead, I'll point out something that didn't stick out even to me at first.
Right now, our ability to fight on a mount is curtailed slightly by our choice of weapon. Greatswords are great, but there's a reason Brettonians consider it a sacrifice that questing knights have to give up their lances; if your opponent is close enough to strike your mount you're way too close to be comfortable. A spear or halberd is just better because it has more reach.
We can't reforge a runic greatsword, and if we did and our opponents got in close anyways we'd be in real trouble because most of our experience is in greatswording and not lancing. In addition, a purely mundane weapon wouldn't be too great with our size and build; unless we could put the weight of our mount behind a spear we'd only scratch up anything actually worth fighting.
Finally, we can't exactly go and ask for another runic weapon to pick up a different style of combat, because that'd be super expensive and it'd require us to carry around a twelve foot long polearm everywhere which would be significantly more cumbersome than a greatsword and fit through less doors.
However, if our dragonbone staff had a hand on the end, then it could just grab on to the end of Branalhune (which we know is light enough to be one-handed, because runic weapons are all hand weapons in the lore and that was translated into the quest this way), and suddenly we've got a sword-spear.
There'd be a lot of mechanical issues with that normally, because holding onto something isn't as strong as affixing it in place, but Branalhune provides its own force upon impact in order to avoid tearing its wielder's arms off, which means we just need to make contact and its runes will handle the rest of the effort. In addition, if it gets knocked out of our staff's hand, rather than either shattering or getting lost, we can just summon our sword back to us and put it back in place.
For the mechanical issues, we'd get something much better than a simple spear. A polearm with a hand on the end would let our staff swing around Branalhune just like we do; it'd have less of a range of motion, but if you think a spear is coming in from a certain angle it'd be quite a surprise to find that it can twist itself in the middle to avoid your guard.