Say I want to get a certificate for my domain, and say that I don't want this to result in the name of my domain appearing in certificate transparency logs or similar locations. (The domain is only for my personal use, and I neither need nor want to advertise it to the whole world.)
What are my options? Do most providers generally submit certificates to transparency logs?
Or do all domains that end up getting SSL/TLS certificates automatically end up on such logs?
I would use a self-signed certificate, but that won't work, because I need to use a third-party service and it needs to be able to authenticate my domain.
Ideally they would be cheap like Let's Encrypt, but I don't even know what my options are.
(Yes, I'm aware DNS logs exist regardless, and I know obscurity isn't security, etc. That's not the point of my question, so please refrain from offering advice on that...)