Can confirm as someone who has to renew a non-Let’s Encrypt cert every year (for reasons). The CA sends an automated email to the email address listed in WHOIS, you click a link in the email, and they issue the certificate. No human interaction necessary.
EV certs have a slightly more rigorous approach. They’ll call the registered agent for the business as registered/licensed with the state, not the phone number from whois or an email to webmaster@