The hard drive, or rather the agent lists it contained, is not merely forgotten. In fact M mentions it to Bond and Tanner after interrogating Silva once apprehended:
Let me know what you recover from his computer. Has he transmitted the lists? If so, to whom? I want this resolved.
This still leaves it a bit open what exactly happened to the hard drive or if the agent names are still out in the open. But what we can conclude is, that during Silva's apprehension, when the whole MI6 was invading his island, they likely consfiscated all of his stuff and computers, so probably also the ominous hard drive. At least MI6 got people working on it, even if not James Bond in particular anymore. Though, even if not captured (rotting in some safe or on some hidden server), it is likely not posing an active direct threat for MI6 (even if still a hot passive danger). Silva was working completely on his own, being an individual self-made Bond-villain par-excellence. So it is rather unlikely that he transmitted the list to anyone or would posthumously keep publishing agent names, because the only use this list ever had to him (and the movie) was as bait for MI6. And after Silva's escape there were certainly more pressing matters for Bond to take care of.
But the fact that it was not referenced anymore later or that the resolution of the whole matter wasn't shown specifically doesn't mean it was not captured, just that it wasn't important for the movie anymore. And in fact, as you already pointed out, it wasn't important for Silva anymore, since it already did its job of putting MI6 and Bond on his trail. So in its true nature as a MacGuffin it wasn't relevant for the further movie either. I'd agree that this might not be a definite answer but only (reasonable) speculation, but sometimes that's the only thing possible for a supposed plot-hole.