The description for use_eip in variables.tf:

Whether to enable Elastic IP switching code in user-data on wg server startup. If true, eip_id must also be set to the ID of the Elastic IP.

In the README there is a mention of eip_id with this description:

When 'use_eip' is enabled, specify the ID of the Elastic IP to which the VPN server will attach.

But the eip_id is never declared in variables.tf and thus never actually used inside main.tf.

By default use_eip = false but when you look at main.tf it will always create the elastic IP internally inside the module. There is no count = var.use_eip ? 1 : 0 as would be expected if the intent is to make it optional.

There is a discrepancy between the README/docs and that main.tf is actually doing.

Q: Is the used expected to create an elastic IP outside the module and pass it in or is the module responsible for managing the elastic IP when use_eip is set to true?