Yes, you are correct on broad terms. Life has no objective meaning. It has a lot of subjective meaning, though.
You loved your cat and your cat loved you. You wouldn’t be upset about this if those two things weren’t true. Does that matter in the grand scheme of things? No, but it matters to you and it mattered to your cat.
I understand where you’re coming from. I have lived in despair after friends, family, and pets have “moved on”. It never gets easier, and I am tearing up thinking about the many moments like this that I have experienced, and the many more that I will experience.
It’s probably very hard to hear right now, but you should soldier through this. You don’t have to, but there are a lot of relationships that you will experience that you don’t even know about yet. There are people and pets that you haven’t met yet or that haven’t even been born yet who you will have an impact on, and who will have an impact on you.
And though this kind of loss is not something that a human can ever really leave behind, one day you will understand it, and you’ll leave a comment like this one. And you’ll know that every relationship we have is valuable (in one way or another) and worth sticking around to experience.
Life is meaningless, but only on a grand scale. The pain you’re feeling now only tells you that life is worth experiencing, even if it doesn’t really mean anything in the end.
RIP to your cat. You probably won’t ever really, “get over” the loss, but this relationship has helped you understand how to love.