Yes that’s the point and yes not having a noticeable difference does not negate the fact that the original person died.
The case of capsuleer resurrection differs from the previously mentioned subject of there being no coherent “you” just a constellation of atoms because the capsuleer resurrection works much like the one in battlestar galactica and how the cylons resurrect (as far as I know).
Only the “consciousness” is resurrected, the state of mind, it just copies that state, not teleports it, unlike in star trek for example where your actual atoms are transferred through a transporter beam, here (as far as I understand and know the lore, which I may be mistaken though) your brain pattern is scanned (and as part of the process is erased / destroyed), the pattern layout plan / “blueprint” is transmitted through hyperspace or whatnot so basically a simple data transfer through “radio” waves, but not an actual matter transfer, then based on that plan the brain is recreated at the destination (either inside the new clone’s head or made separate then inserted to the clone, not entirely sure of these specifics).
Thus even without the immortal soul / spirit / whatnot (which I deliberately did not mention so is just a purely materialistic philosophical discussion) the original matter and its composition is destroyed which means the original person is dead.
Unlike in case of when you go to sleep and wake up next morning or simply have your cells constantly be replaced by others as part of your biological existance so even without having your consciousness “interrupted” you basically constantly die as an individual but constantly exist still as a whole.
But in case of the capsuleer resurrection you die as a whole as well and are just copied (your brain pattern specifically) but the original composition of atoms is lost, destroyed, thus even the whole “you” is dead and just a copy is created as a substitute.
In a spiritual sense it can be argued that this copy can be considered as part of the whole but that is a different subject altogether and strictly from the whole “you” sense the old person is dead regardless.
I also recall some EVE books / fiction that had a capsuleer (or even several not sure) cloned without the old clone destroyed though I only read people discussing this and not the actual story they discussed so not sure of those details either, though it seems to align with what else I read about the subject so seems fitting, which also confirms that it is not matter that is transferred just the pattern that is then used to construct a new brain at the destination.
So unless your spiritual concept is that copying your brain (and body) even at a quantum level results in You being duplicated it is clear that the clone / copy is not the original person, just a replica.
You may have the “spiritual” standing that the other copy is you as well but that is a whole different argument and requires defining what is “you” even in the realm of materialistic only philosophical discussion (so no soul / spirit / whatnot involved) as the answer whether the copy is you or a different thing depends on the definition.
Arguments can be constructed both in favor and against and which argument is right / correct depends on the definition of what is considered to be “you”.