The question of whether they have qualia is distinct from the question of whether one of them must be the unique inheritor of your STC.

Yes, you're right. You're describing a "branching thread of consciousness" model. Next, can there be a branching-and-merging model? Does it even make sense to ask the question?

If STC is a purely subjective experience unobservable from the outside, then we can't really count the STCs. We may not be able to actually assert that the number of STCs at time n+1 is greater than at time n. In other words, we don't really know if STCs can branch and/or merge even in our actual universe.