Xcode does not detect new Apple Distribution Certificate in my keychain
You need to obtain the private key for the certificate before you can use it for signing with Xcode.
When using Keychain, the private key is generated on the computer that was initially used for creating the certificate signing request (CSR) that is sent to Apple in order to obtain the certificate.
You need to copy the private key from that computer to your current computer in order to be able to use the certificate with Xcode.