Gateway endpoints are free. Network endpoints (which are basically AWS-managed ENIs that can tunnel through VPC boundaries) are not free.
S3 can use either, and we recommend establishing VPC Gateway endpoints by default whenever you need S3 access.
(Disclaimer: I work for AWS, opinions are my own.)
The original private endpoints implementation required meaningful work from the service teams (ec2 networking, s3, & ddb). It also changed how the "front end" API servers handled requests and how their infrastructure was deployed (at the time?). The newer LB/ENI style privatelink abstracts away _most_ of that "per service" implementation effort at the cost of more per-request/connection work fromthe virtual network. Hence why theres more support from other services, and it includes a cost.
I think that is by design https://konghq.com/blog/enterprise/api-mandate
Why don't you have gateway endpoints for all your APIs?