"There are souls" is not an explanation of how they work.

But of course that is an explanation, in the same sense that Maxwell's equations explain the behavior of electric and magnetic fields. "We have this here thing, and is generates this here other thing, which is an observation we describe with this here equation". No different (disregarding the complexity penalty) from saying "souls generate experience" and if all you miss is the math-speak, then insert some greek letter for "soul" and another one for "consciousness". Of course, there is no reason to posit that 'souls' exist in the first place, given the commonly accepted definition. However, the concept of souls doesn't get discarded because it doesn't explain consciousness, because it does. It gets discarded because it adds complexity without making up for it by making predictions, or simplifying the descriptions of the available data/experiments.

As for myself, I simply note the evidence above, the problem it leaves unsolved, and my lack of any idea for a solution.

A common error with the (to me) best candidate explanation, panpsychism, is that it is often conflated with "everything is conscious, so everything thinks / has a mind / is agenty in some sense / can suffer". Obviously matter has the potential to generate qualia, at least in certain configurations. It seems, just on complexity grounds, a simpler model to posit that consciousness-generation is just something that matter does, rather than something which happens exclusively in brains or other algorithm-instantiators (not unlike Tegmark's thought process leading up to "Our Mathematical Universe"). Brains just have the means to process / consolidate and report it. Consider if it were so, then evolutionary selection pressures would work on that property as well; leading to e.g. synchronizing individual "atoms" of consciousness into larger assemblies (cool guy).

Of course, the distinction between the uncontroversial "matter has the potential to generate consciousness" (which the process-folk would also agree with) and "all matter generates some proto-form of consciousness, and the brain evolved to synchronize and shape these building blocks" may be merely a difference in phrasing. Nevertheless, I lean towards the latter purely because it seems simpler in an algorithmic complexity sense. (These are abridged thoughts, the in-a-nutshell version. There are weak points, such as model-building and consciousness being linked in some sense, otherwise there would be no selection pressure to consolidate consciousness. Still, I feel the 'it's an emergent property' to be much more flawed. We forget that emergent is just code for 'can't grasp it on a more basic level, a shortcut our computationally limited models are forced to make. A computationally unlimited model-builder could do away with the whole 'emergent' concept in the first place, and describe a chair -- or a wave in the sea -- on the most basic level. Concluding that something is emergent in the sense of saying it only exists on a certain level of granularity upwards is, to me, confusing our very useful model-building hacks with the reality they aim to describe. There is no 'emergent' in reality. There is only the base level, everything else is a computational hack used by model-builders.)