I heard a discussion of this issue which made a useful comparison - that brains are not clockwork but more like a steam engine, with information as a 'working fluid'. That is, we are not just the infrastructure which can be in a stable or frozen condition, instead we are something dynamic, a constantly updating state integrating many ongoing processes. So you say atom arrangement, fine. But also currents & waves moving through us.
Human resuscitation is a very interesting area, with a lot of recent progress. There are indications humans may be able to hibernate, lowering core body-temperature & other bodily processes including mental activity, to dramatically decrease calorie consumption. Maybe if we can understand more about how to safely shut down this might help. They are talking about using this state for space travel, and for surgery.
I feel until we get closer to understanding brains & making analogues, we are just giving opinions. You should note atomic-fidelity is not required for cellular-scale organisation, but also that we likely need to understand ongoing processes not just momentary states.
As a Buddhist, the idea identity is a process not a state or essence separate to processes, is very familiar. Who is 'really' who would be about legal definitions, custom, and emerging practices to deal with real tensions in practice. In a very real sense we can be only loosely connected to who we used to be in our own lives - the continuity might be greater for onlookers like parents, than something we experience ourselves..