For every cloud provider, we have different ways of looking at logs (i.e., Cloudwatch for EKS, this for AKS etc).
It looks like I can easily transfer the logs from Cloudwatch to S3. Do AKS and GKE can expose their logs collecting applications through APIs? I'd like to transfer the logs from all cloud providers (EKS, AKS, GKE) to S3.
On AKS, if the monitoring is activated, Microsoft will deploy a wrapper around Fluent Bit to send the logs to Log Analytics. You can then use the Log Analytics API to fetch the logs. On GKE, you can do something similar with the Cloud Logging API.
Whit that said, your best bet would probably be to install Fluentd or FluentBit on all your cluster and send your logs directly to S3.