There are actually numerous issues that can cause the deploying state to time out after the 3600s timeout. The error presents in your execution log as...
2022-03-03 07:50:25 : Deploying state timed out after 3600 seconds
This article is specific to a problem where the autoscaler will trigger scale up of a new node, but the new nodes will fail bootstrap and never join the EKS cluster. Check if you are using kubectl v1.24.0 in your user-data script in AWS or you are pinned to the latest stable release, https://dl.k8s.io/release/stable.txt. At the time of this writing the stable release is 1.24.0.
Then you may be running in to a bug in kubectl v1.24.0, https://github.com/aws/aws-cli/issues/6920. The remediation is to pin your kubectl version to v1.23.6. Later versions than kubectl v1.24.0 should contain a fix, so if you are on a later version this is not likely to be your issue.