How this check works
The tool looks for names shaped like example.com, including the ones inside links and email addresses. It lowercases them, drops the www prefix, and removes repeats.
Each domain is asked for its name servers, its address record, and its mail record over encrypted DNS. Any answer means the domain is registered.
Records found means taken. A name error from DNS means the name does not exist, so it is probably free. Anything else is marked as no records, which you should still confirm.