How can someone "reference" an old certificate with CT data? CT logs only contain precerts and certs, right? I suppose one could compare the public key of two

How can someone "reference" an old certificate with CT data? CT logs only contain precerts and certs, right? I suppose one could compare the public key of two leaf certificates, but reusing the private key is also a bad practice. From CA end, it could check if the certificate is requested from the same account key. One can even use a DNS record to public the account keys (CAA + TLSA).