That’s a fantastic question!
There’s archeological evidence that modern humans were far more mobile than we have generally assumed (see eg David Graeber), but we’re talking 10-20k years ago there, which is very recent in evolutionary time where we’d be talking about physical adaptations.
SJ Gould, who was the origin of the spandrel idea, warned frequently against telling “just so” stories to try to reverse engineer the processes of selection that led to this or that feature. However, I do think that the hominid physique enabled multiple things. It has been observed that you won’t ever see a spider or octopus or dolphin moving fire from one place to another. That’s something that bipeds are able to do, and fire is one of the things we think was a key development. It’s the same with generalized tool use. So we can see there may have been multiple selection pressures leading towards bipedalism.
If distance running were truly a spandrel, we’d have to say that it was a consequence of these selective pressures giving rise to the body plan, but wasn’t itself selected for. I’d be more conservative on that one, and hazard a guess that distance running (or efficiency in long distance movement) was also a selective pressure. I just don’t think the evidence is there to say that it was the dominant one at that time.