I would look into the ApiUser and if the attribute client_cn really matches the cn in the subject of the certificate shown with openssl x509 -noout -text -in CERT.
If you want to reuse the agent’s certificate, an ApiUser for each System would be needed.
But I would recommend one ApiUser for one functionality and then distributing the certificate, for example in one environment we have a downtime user with permissions restricted just for this use case. While Icinga 2 has no revocation list and so you can not revoke the certificate, by removing or changing the ApiUser you can remove the permissions quite easily.