VPC - internet gateway related

Hello.

There is no charge for the Internet gateway itself.
https://docs.aws.amazon.com/vpc/latest/userguide/VPC_Internet_Gateway.html#internet-gateway-pricing

There is no charge for an internet gateway, but there are data transfer charges for EC2 instances that use internet gateways. For more information, see Amazon EC2 On-Demand Pricing.

It is possible to create a default VPC, but there is no way to create a default internet gateway as far as I know.
Therefore, if you have deleted it, there is no problem by using a manually created Internet gateway.
https://repost.aws/knowledge-center/deleted-default-vpc

Internet Gateway is simply a logical router to the internet for a VPC. An internet gateway provides a target in your VPC route tables for internet-routable traffic. once you delete it you need to create a new one.

There is no charge for an internet gateway, but there are data transfer charges for EC2 instances that use internet gateways. https://aws.amazon.com/ec2/pricing/on-demand/

If IGW is not configured in Route Table, then there is no traffic flow and it does not incur any charges in your bill.