I believe Gateway API was meant to be v2 of Ingress API. Also, as per the documentation for Gateway API:

The Gateway API was originally designed to manage traffic from clients outside the cluster to services inside the cluster -- the ingress or north/south case. Over time, interest from service mesh users prompted the creation of the GAMMA initiative to define how the Gateway API could also be used for inter-service or east/west traffic within the same cluster.

The existence of https://github.com/aws-solutions-library-samples/guidance-for-external-connectivity-amazon-vpc-lattice and the following excerpt:

When you create a VPC Lattice Service, you are given a DNS name that represents it (globally unique and externally resolvable). However, from outside of the VPC, the DNS name resolves to a series of IP addresses in the 169.254.171.x/24 range (within the IPv4 Link-Local range 169.254/16 defined in RFC3927) and fd00:ec2:80::/64 range (within the IPv6 Link-local range fe80::/10 defined in RFC4291).
seems to indicate that aws-application-networking-k8s

indicates that this Gateway Controller (which relies on VPC Lattice) only implements east/west traffic at the moment.

Could this controller be extended to support ingress (north/south) traffic?

It almost seems to me like aws-load-balancer-controller and this controller may need to merge in some way to fully support all Gateway API capabilities. (Related: kubernetes-sigs/aws-load-balancer-controller#1338)