What is the basis for your claim that an animal has no rights? I’d be glad for a bit of elaboration on the topic.

I’d also be glad for some elaboration on this. Do human beings have a right not to suffer? If so, why don’t animals, who feel like humans do, have a similar right?

Do you have an explanation for why telephone poles or gravel stones have no rights? Alternatively, do you have an explanation for why human beings do have rights? These things are fundamental principles, and I don’t see either a possibility or a need to explain them.
Rights belong to human beings as creatures whose lives have value and toward whom there are moral obligations. Animals do not have rights because they are not entities with free choice and value, in my opinion. We are obligated not to cause them pain and not to let them suffer, but that is not their right; it is our duty.
It may be that the distinction between rights and duties is not clear to you. See more about rights and duties in my article:

בין הטריטוריה שלי לטריטוריה של הזולת על חובות וזכויות בהלכה ומשמעותן

Michi, I’ll allow myself to make the following comment:
I think more or less like you, that animals have no rights, except that I don’t understand and/or don’t agree with your reasoning.
On the one hand, you determine that these are fundamental principles and therefore there is no possibility or need to explain them. On the other hand, you nevertheless do give a reason why, when you say that they (the animals) do not have free choice and do not have value.
What I think is hidden at the base of your claim is the idea that animals do not have a “soul,” or at least not a soul like that of human beings. Someone who has a “soul” would presumably also have free choice and values.

I defined; I didn’t justify. I have no justification for why only creatures with free choice and consciousness have rights.

Since you used wording of causation (“because”), I allowed myself to interpret your words in the irresponsible way typical of me and assumed that it wasn’t a definition but a justification.
As for the matter itself, if you, as a dualist, accept the claim that in a human being there is a non-material side, and if you agree that animals do not have such a side, then you won’t have trouble entertaining the use of the word “soul” to explain the matter of rights.

Thank you very much, Rabbi.
How does the Rabbi define consciousness?
How do we know that animals don’t have it?

I’m not sure they don’t have consciousness, but presumably not at our level. Beyond that, consciousness alone is not enough to be a creature with rights. Free will is also needed, and it seems to me that animals do not have that. Although that too can be debated. On the face of it, that is how it seems and that is the accepted view, and people are executed and stoned on the basis of presumptions.

Why is free will a criterion for having rights?

Let me clarify my question:
I saw that you wrote in an earlier reply that you have no justification. So is the determination simply “empirical”? You see that you attribute rights only to beings with free will, and therefore generalize and determine that this is so?

A basic intuition.