What are the types of VPC endpoints?

No, you cannot attach security groups to a Gateway VPC endpoin

Do VPC endpoints support cross-region access

No, VPC endpoints do not support cross-region access.A VPC endpoint enables private connectivity between your VPC and supported AWS services within the same region, without using the internet or NAT.

Which AWS services support Gateway Endpoints?

Do VPC endpoints support cross-region access

Can you attach security groups to a Gateway endpoint.