Neither the GDPR, nor the CCPA, nor any other data protection law that I am aware of, requires that when information is deleted on request, that simiansimilar information not be collected and stored in future. Under the GDPR Article 6 there would have to be a lawful basis for any processing, including storage, assuming that the GDPR applies to the directory in question. There could be a claim that such processing was lawful under article 6(e) "performance of a task carried out in the public interest". I do not know if any such claim has been adjudicated.
Thus there is no need to hold a database of previously erased records to determine if a new record should be blocked as "previously deleted".
The Wikimedia Foundation, which runs Wikipedia, I believe takes the position that the GDPR does not apply to Wikipedia, I am not sure of their detailed arguments. But surely articles on well-known people, such as a former US president, would be covered under the same provisions as would cover news reports and historical books about such a person. Perhaps that would also come under article 6(e)