Hi Romain,
Thank you for the details it helps a lot!
The search override feature was disabled. That means the default WooCommerce results were displayed. The keywords must have matched somewhere in the content or a custom field – it is not possible to search the domain name, it is very likely stored somewhere.
Anyways, I have enabled the override, now you should start seeing more relevant results.
I also recommend updating the plugin sometime because it is outdated.