At the minimum, you need the following enabled on the user profile that pushes into the container registry:
"ecr:BatchGetImage",
"ecr:CompleteLayerUpload",
"ecr:DescribeImages",
"ecr:UploadLayerPart",
"ecr:InitiateLayerUpload",
"ecr:BatchCheckLayerAvailability",
"ecr:PutImage"
At the minimum, you need the following enabled on the user profile that pushes into the container registry: