Then what do you believe the soul is?
It's difficult for me to answer this, for a couple of reasons. The main one is that, when I do, it sounds like a truth claim. But it isn't. I am well and truly agnostic. So, while I have some "beliefs" on the subject, they're entirely Faith. No objective evidence, although I avoid beliefs that contradict what I do have evidence for. To me, Faith is(very broadly speaking) beliefs people hold because they prefer that they are true. As opposed to beliefs people hold due to compelling evidence(proof).
So, what I'm going to describe here is what strikes me as the best plausible explanation for something, which remains a huge mystery. But, I doubt that it's objectively true. Because I'm confident that, being a limited and fallible human being, I do not, maybe cannot, understand the objective Truth on these matters. My views are simply what I prefer to believe.
Anybody else might not prefer them, that's fine with me since I don't expect anybody else to mistake me for an authority on the subject. I don't think anyone is, despite all the claims made by religious folks.
So, all that said.
I believe that humans, all living things, are animated by a "spark of God". Call it a Spirit, a soul, nobody really knows much about it and maybe never will. So it doesn't matter what word symbol we apply. That bit of God, combined with some matter, form a human or organism. When we die, that bit of God separates from our material selves, our meatself, and merges back into God, the Ground of Being.
That bit of God doesn't cease to exist, any more than a raindrop falling into the ocean ceases to exist. But neither will it ever exist again as a separate thing. What ceases to exist is the illusion of separation from God. That raindrop was never really separate from the ocean from which it came, it just seems like a separate body of water due to the limited perceptions of humans. Death is the end of that illusion.
Similarly, our meatself continues on in the vast cycle of transformation that is the material universe. In the short term, say the next couple of billion years, it will nourish other living things. Eventually, it will wind up in the sun, likely being fused into heavier elements before being blasted into space in a supernova.
Death is the end of the illusion of being separate from God. The end of our individual identity, which is a delusion caused by the illusion of separation from God. We won't just see our loved ones, in the limited way we do while experiencing the illusion of separation from God. We'll be part of them and they us and we'll all (from pets to your mom to Hitler to Van Gogh) be part of God.
That's the kind eternity I prefer to believe in.
And it makes far more sense, to me, than any of the other claims I've heard on the subject.