I have some understanding of how PKI works, similar to this: - https://knowledge.digicert.com/solution/SO16297.html - https://security.stackexchange.com/questions/59566/ssl-certificate-chain-verification - https://security.stackexchange.com/questions/56389/ssl-certificate-framework-101-how-does-the-browser-actually-verify-the-validity
What isn't obvious to me is how the public key at the end of the chain, or the identity certificate is used. Previously RSA may have been used for encryption, or as the key exchange for a symmetric cipher key, however ECDHE appears to be the modern primitive for key exchange.
My guess is the certificate is also signed by itself, along with the intermediates and roots in the chain. This would make sense to me since in my mind anyone would be able to use the cert in various ways, however if signed with the private key of the identity it's an extra check. Other wise I would see the identity private key as being pretty useless.
Most explanations are very simple with how a chain is evaluated and I'd like some detail.
So my question - is an identity certificate also signed by itself? Does my logic above stand up?