Specifically, the Auto ISO "Minimum Shutter Speed" is the threshold when Auto ISO kicks in and starts increasing. Normally in usual practice, as the light becomes more dim, the shutter speed falls. But when it hits this threshold, then then it holds there, and Auto ISO starts increasing instead. When ISO hits Maximum, then shutter speed has to continue its fall.
What that means is that any active Auto ISO picture (when ISO is moving, between Minimum and Maximum) will use that Minimum shutter speed. Auto ISO will increase, but this shutter speed will be held, as long as possible. So this shutter speed has importance, it is what will be used.
Auto ISO does not really try to stay low, instead when active, it simply does what it must do to try to hold the proper exposure. I suppose it does try not to overexpose.
But Auto ISO is always a last resort, only active when at a hardware limit and all else fails. The real hardware limit is the 30 second shutter speed, but that is hopelessly impossible to handhold, so they added this new shutter speed choice to use as a limit. Auto ISO does try to hold this minimum shutter speed as long as it can. Give it some thought, it is what will be used (if Auto iSO is active).
What Auto does there (as shutter speed) is to set this minimum shutter speed threshold to be the standard 1/focal length shutter speed for FX, for example like 1/50 second for a 50mm lens. Or 1/(focal length * 1.5 crop factor) for DX cameras... for the current lens zoom in use. Considered a minimum that most people might be able to handhold steady if they try hard, but it is just a guideline, not an absolute. We might have other opinions.