We were not aware that, even if incoming traffic to S3 is free, if you are sending data from an Ec2 in a VPC with a NAT, then you pay for the NAT traffic!!
The solution is to use a free Gateway endpoints for Amazon S3, and you can save a lot https://docs.aws.amazon.com/vpc/latest/privatelink/vpc-endpoints-s3.html
(I wonder why it is not enabled by default)
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Do not waste $ on NAT traffic when you read/write to S3 | Heykuki News