I think a definition of the security of a signature scheme is that a computationally limited attacker should not have a non-negligibly better than chance guess of the secret key.

I think some of the “ZKP” techniques are supposed to only be “ZK” for a computationally limited observer? Though I may be mistaken, and maybe non-interactive ZKP schemes are only assuming that the prover has limited computational resources, not that the observer/attacker hoping to get information from them does?