Earlier quoted context omitted.
X509 certificates published in CT logs are "pre-certificates". They contains a poison extension so you don't be able to use them with your private key. The final certificate (without poison and with SCT proof) is usually not published in any CT logs but you can submit it yourself if you wish.
Although the poisoned pre-certificates† are logged as a necessary part of offering the least hassle product which is the business Let's Encrypt are in, they, like most CAs, also log the finished certificate shortly after. Here's the pre-certificate for this web site's current certificate: https://crt.sh/?id=23696530376 and here, just a few later in the log, is the finished certificate: https://crt.sh/?id=23696528656…
Happy to see LE publish both, but others do not. Here is an example: https://crt.sh/?id=17293798014
Your won't find final certificate from digicert/globalsign in the CT logs.
Unless the owner publish it himself, API is opened for submission I think for everybody.