You can check Cronjob completion/failure by pods status only. However if you want to verify you can check by logs also if you have enable logs from EKS dashboard which will push logs to cloud watch and check the logs of cronjobs.

Also you can do something like :

kubectl get jobs <job-name> -o json | jq '.status.conditions'

but please just keep in mind Jobs never Failed (its Pods terminated with error doesn't mean the Jobs has Failed

How to get notification on job failing :

https://medium.com/faun/how-to-get-notifications-when-kubernetes-cronjobs-fail-ed4ca4313e81