API charges of moving data from S3 Standard to S3 Glacier Deep Archive

You are only charged for Lifecycle transition requests, not for GET or PUT requests, when using Lifecycle rules.

You can check the prices here. The cost depends on the storage tier to which you transition your objects and the region in which you are located. You will pay x.x$/1000 objects moved.

For example, if you want to use s3 lifecycle rules to transition objects to S3 Glacier Deep Archive in the N. Virginia region (us-east-1), you will be charged $0.05/1000 objects.