I would also add that it seems that rights are a human concept/social construct, even just in the sense that we're interpreting what we believe to be ethical/right/moral, even if it's objectively correct; or we're enforcing laws based on what people believe is correct, or in some cases what serves certain people personally at the expense of what most people believe is right if the laws are corrupt/undemocratic.

So I think if we're going to claim that a certain right "just is", since we're the ones creating these concepts even if it's based on our observation of the world and an interpretation that was theoretically objectively correct if not a belief, it falls on us to rationalise and describe how we're coming to these conclusions and what we're basing this assertion of a certain right on. Otherwise, "it's a human right because it's a human right" is just circular reasoning and has no explanation. How are we formulating our basis for what is a human right? Is it legality? Is it moral beliefs or what we reason (or even logically prove somehow) is objectively morally right? Or ... what?

For example, in the case of animal rights theory, many people believe that there are moral rights that animals hold as moral patients, i.e. "negative rights" (= freedom from something being done to an individual) not to be exploited and killed by humans (moral agents), which extend logically from the belief (or fact) of human rights also being morally correct. And in this view, humans by way of our laws, do hold legally the "positive rights" (= freedom of an individual to do something) to exploit and kill animals, but these legal rights are simultaneously violating the moral rights of the animals to not have these things done to them by humans/moral agents.

In this case too, similar to what you said about the human condition, we could argue that something about the condition of animals (which could for example be sentience/consciousness, which they share with humans who are also animals), is the basis for them having these rights, but even then we're still speculating based on what we believe is either subjectively or objectively moral (since in that case obviously what's legal is in contradiction with what's deemed to be moral), and I'm not sure what third definition of rights could be being applied there whether it be in the context of human rights or animal rights.