I would freeze them after soaking and then cook them once they are defrosted. The freezing process can make them softer than you expect when they defrost. So if you cook them perfectly, then freeze them, they could be too soft once defrosted.
I cook then freeze them. We basically eat black beans plain (i.e., "soup" or on rice), so I would not call the beans "mushy" after freezing but I will say that the soup tends to thicken up sometimes, which in many cases is way yummier. I wouldn't say the same for other kinds of beans, but black beans freeze particularly well, in my experience. Plus the flavors meld more, also a big plus for black beans. Yummy!