As such, Apigee Message processors will need to store client key and certificate in a keystore and send this to the target service which would need to verify same in order to establish a TLS connection
Can you confirm this is the desired configuration? If so, please elaborate on why a CSR process is needed - usually, the external provider at the target, would provide you with a client key and certificate to load into a keystore at Apigee for use in mTLS configuration.
If your team is maintaining the target service also and is wishing to generate a CSR and private key to provide to a signing authority in order to obtain this certificate, most signing authorities have tutorials and even wizards for this. You can use openssl, java keytool, etc. SSL Shopper has this handy guide for using OpenSSL to generate a CSR and private key.
Work with your internal PKI group (public key infra) for certificate provisioning who can guide with the CSR process. Follow below to enable 2-way ssl from apigee to backend service.
Not sure what’s the thought process in general(if you comparing some other products :)) you need to procure certs (by internal /external) then you can just follow the instructions from the docs to to upload the certs and setup mutual tls.