> one by one these neurons are switched off with their functionality offloaded to their clone instantiated in a computer.

We are not just brains in a jar. Our bodies provide rich sensory information, and feedback loops without which we would definietly not be “us”.

To use the “Ship of Theseus” analogy you are proposing to replace all the parts of the cockpit with new parts, but you are also at the same time discarding the hull, the sails and the oars. It would not be the same “ship” without those other things. You also need to very precisely replicate/simulate those parts too otherwise you won’t have the same person.