Although this may not be related: Are you using a S3 Gateway Endpoint for your backups? If not, you should. It will mean that traffic from your instances to S3 will not have to go through NAT Gateway. This will reduce cost as well as reduce the amount of traffic through NAT Gateway that is going to S3.
Otherwise, at this distance it is difficult to determine what might be causing the traffic spike. I'd recommend enabling VPC Flow Logs to try and determine if there is something in the VPC which is causing the issue. You can use Athena to query the flow logs.
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