Yes. But usually "we" (see below for an explanation of why that word is in scare quotes) use the word "computable" in a context where quantum computers are not even in play. Quantum computers have only become a thing fairly recently relative to the amount of time that humans have been talking about computation.
This entire conversation turns on the meanings of fuzzily or implicitly defined words like "useful" and "almost" and "we". But the whole point of quantum computers, the only reason they are on the radar, is that they can potentially do something that classical computers can't do for some not-entirely-unreasonable definition of "can/can't do" and (and this is crucial) that WE MIGHT ACTUALLY BE ABLE TO BUILD ONE THAT REALIZES THIS THEORETICAL POTENTIAL. The jury is still very much out on that, but it's looking more promising than many skeptics imagined a few years ago.
You wrote:
> There are a number of formal models of "hypercomputation" that could compute things that a classical computer can't compute
Yes, that's true, but irrelevant because none of these formal models are physically realizable so no one cares about them (except theoreticians).