Even if your work is hosted locally, WordPress transmits its URL during updates, possibly exposing project details and your IP to external parties.
I noted similar behavior when running WordPress on a local server for development. Although transmitting the URL may not immediately seem critical, it raises concerns over privacy and exposure of non-public project details. One should consider potential risk factors, especially if the local development involves sensitive configurations or industry-specific topics. It can be worthwhile to investigate possible workarounds provided by the WordPress community. Adjusting update preferences or utilizing alternative configuration settings might help reduce external communication during non-public testing phases.