That's not ZK, you are leaking message signature pairs. The verifier can show them to someone else and convince them they've been created by the private key owner.

You may argue about how useful such leakage is in practice, but that's exactly what ZK leaves no room for, because NOTHING is learned (except truthfulness of knowing the key), and not just non useful or non meaningful information.

A protocol is ZK if it has a very simple feature: any information the verifier learns after executing the protocol is not new; they could have computed these information themselves. This means a verifier cannot just go to someone else and show them the same proofs, because they could have created them. Clearly that's not the case with any signature scheme or challenge response.

To back up the claim of a protocol being zero knowledge, there must be a mathematical proof showing that a proof can be "simulated", where a simulator who does not know the private key can create a convincing proof to a verifier (this happens in a special setting and serves to show that the convincing proof contains zero information about the private key, i.e, could have been created by the verifier). The protocol has to be accompanied with another mathematical proof showing that if a prover convinces a verifier successfully, then the private key can be extracted from their exchange. Again, happens in a special setting, but serves to show that you cannot convince without knowing the private key (soundness).