This is usually the case, for example, when considering signing transactions or signing messages and reusing the k value. In such cases of re-used and non-random k values, it is possible to derive the associated private key, as you say.

This is not the case here, however. Encrypting a message in this way only requires knowledge of the public key, not the private key. Otherwise, how would you encrypt a message to send to someone else? There is no way to derive the private key from this encryption process, even with reuse of the ephemeral key.