How do you know that you have sustained consciousness at all?
Your body is something like the ship of Theseus. Your brainwave patterns are constantly changing, the matter in your brain is constantly rearranging and being replaced. Isn’t it possible that sustained consciousness is entirely an illusion caused by our persistent memories of past selves?
What if every time you go to sleep, your consciousness actually ends, and every time you wake up, a new consciousness is instantiated with the memories of the past consciousness?
I find that it’s better not to think about it for too long.
On the other hand, what if the feeling of changing bodies is similar to that of simply falling asleep and waking up again?
There is the problem of multiple “you’s.” However this might only be a problem due to our own preconception. After all, it’s possible that your “soul” (by which I mean your continued consciousness, or your unique experiential vantage point) can actually exist in two places at the same time.
For instance, if you travelled back in time and met yourself, you would technically exist as the same soul in two different bodies.
Maybe cloning splits the timeline so that you exist in both bodies simultaneously in a similar way.
Maybe the same soul can exist in different contexts at the same time.
It’s also possible to think of the soul as something ever changing, a thread. In that case when you go back and meet yourself, you are looping the thread back on itself, but the two thread points that meet are actually unique from one another. In the case of cloning consciousness, one might be “splitting” the thread, which is hard to imagine.
I think its likely that splitting the thread would lead to individual consciousnesses moving forward, but I don’t know that it’s the only option.