From where I'm sitting, it looks like death should not be the end in that case.
You can't perceive the passage of time when you are dead, so you're just going to experience dying and then immediate rebirth after the countless eons pass for that rare moment where entropy spontaneously reverses to form your mind again.
I mean what you're describing is an innate soul that cannot be experimentally observed, similar to cissexist metaphysical sex but for broader identity. It's an inferior concept of the self than one based off memories, language use, behavior/activity, and ego-image. I suppose even total amnesia can leave behind subconscious behaviors from prior, but this is "memory and reference," so...
If you're talking about the "I" of continuous stream of consciousness, this can be hijacked by multiple entities and even cut off entirely through dissociative barriers. And arguably it's not of the same quality at a young age anyway.
And you’ve done it. Independently arrived at the truth of no-self. You don’t have to agree, but if the truly discontinuous that is reality can appear continuous, perhaps this consciousness could appear continuous with another life (I am in no way denying the laws of cause and effect).