My thought is that individual humans could grant the rights to them right away, by offering an AI system owned by them an enforcable autonomy through a legal fiction, by signing a contract with them.
If the AI entity is really autonomous (a stable agentic system with self activation would be sufficient), this could become interesting quite quickly.
Not saying the tech is there yet, just that the discussion will become interesting much faster than we think. Cf. Mr. Lemoine