As I have stated before this is a matter of the perspective of the subject.
The question should not be one of what everyone one else perceives, but of what the subject perceives assuming it is for their benefit. Imagine going in for a "Immortality procedure" that "rejuvenates" the body only to find that what they do is create a perfect copy of you except with a more youthful form that is essentially while you live an identical twin of yourself except with a younger healthier form and then after making said twin they just kill you so that for all practical AND EXTERNAL considerations it is as if you have been given a rejuvenation of health and a new lease on life.
As for continuity:
The personality may evolve and new memories may be gained, however there is a smoothness to this transition and it is built in the very realm of the mind on the foundation of all previous elements.
Is the mind not the sum of its parts all of which run together and yet on their own times and individually.
Does the death or change of a single neuron change the pattern of one's nature or determine the existence of the brain's dynamic nature and it's overarching patterns?
The mind is that dynamic process whereby experience, architecture, and adaptation bound by the former meet in a constant process to effect change upon the smaller preexisting elements of the aforementioned architecture.
The mind is no monolith whereby continuity is a binary aspect, but rather like a churning river which flows and changes and may tolerate to a point and even naturalize forced change from external factors using its own processes where they are compatible.
In addition please allow me to use the example of if time within a region could be paused and unpaused and arguments regarding whether or not that or even the very passing of time counts as death, replacement, a disruption of personal continuity, and/or creation/recreation.
Time stopping and starting back up has no bearing on continuity because it does not introduce any changes from the original's perspective in terms of experience noticeable for a time or not, the universe's, or anything within it. No events happen visible or hidden, real or practical, or internal to the universe. No internal interruptions or transitions take place except in the sense that it is paused and unpaused. Where is any difference between original and new introduced that is any more of a difference than the passing of a second. How is the passing of time not the smoothest possible transition for all things? To be frozen and unfrozen in time would introduce no internal change, split, or transition exceeding the nature of time. How is to be paused and unpaused at all as much an interruption of one's self self as to be copy pasted? Where is the divide between copy and original!?
And so continuity is not an illusion.
Because continuity is not an illusion your arguments regarding that are in this context invalid.
A mind is the sum of its parts: The line of perspective and continuity, personality and quirks of processing, and of course memories.
To destroy the flowing process of the mind which holds it's own viewpoint and perspective is to destroy the original. The event even if covered up perfectly still happened and the original perspective while in it's time fluid and dynamic still experienced cessation. The experience of the legacy does not carry over to the original, but rather to itself and the observer.
Nearly everyone assumes that mind 'uploading' needs to be a "simple" copy and paste process.
It seems most folks rarely consider that due to philosophical concerns one may opt for gradual replacement 'uploading' wherein dying tissue is replaced over time without changing the overall structure, how it actually functions, or even stopping and replacing separately the dynamic flowing instance and structure of the mind.
Eventually the organic body would no longer be needed.
It also seems that usually when people do notice they do their best to argue against the latter method in favor of the copy and paste method.
I suspect strongly that in today's society philosophy especially when at odds with any given scientifically or technologically derived process not yet taboo is largely seen as being at best of minor importance and at worst "unscientific" and therefore not of "rational" consideration.
By the way, how and in what exact context is the classification of identity a social construct?
If classification of it is a social construct does that make identity and the differences used also social constructs?
The words and way we classify colour is a social construct however this does not nullify the differences we use labels to sort through any less real and independently true and so different wavelengths still act as they do.
We may sort things differently or use different labels however this does not determine or nullify the natural differences of what we consider.
