AWS Lambda (Serverless) vs. Elastic Kubernetes Service

I have got a scenario for Product Service in a typical eCommerce cloud based application on AWS using say .Net 6 Microservices (we can use other tech stack also), which has to provide some required business functions such as add, edit, delete and search catalog on various input combinations such product name, category, price ranges, ratings etc. Now there are two solution options in my knowledge:

  1. Create two Microservices- one for product service for add, edit, delete and the other for catalog service to search catalog both using docker containers and Elastic Kubernetes Service orchestration.
  2. Create AWS Lambda for each business functions like add, edit, delete and search catalog.
    Please suggest when and.where the above solution(s) should we choose. Please suggest if there is any other solution for it. Also please clarify when to use AWS Fargate for this problem statement.