I think Fargate is included in SES. I can find no direct reference but several indirect references so your mileage may vary. Here's my logic:
What is Fargate
AWS Fargate is a serverless compute engine for containers that works with both Amazon Elastic Container Service (ECS) and Amazon Elastic Kubernetes Service (EKS).
What is ECS
Amazon Elastic Container Service (ECS) is a highly scalable, high performance container management service that supports Docker containers and allows you to easily run applications on a managed cluster of Amazon EC2 instances.
What is EKS
Kubernetes groups containers into logical groupings for management and discoverability, then launches them onto clusters of EC2 instances.
From the references above Fargate utilizes ECS or EKS. ECS and EKS are both clusters of EC2 instances.
As you pointed out, SES for EC2 users has a free tier.
Bottom line: by inference Fargate is basically clusters of EC2 instances which are a requirement for the SES free tier.
SES Free Tier