Which AWS service or feature should the engineer use to simplify and scale this connectivity as the VPCs increase in number?
VPC endpoints
AWS Transit Gateway
Amazon Route 53
AWS Secrets Manager
Explanations:
VPC endpoints are used to privately connect a VPC to AWS services without using an internet gateway, but they do not scale connectivity across multiple VPCs in a hybrid cloud environment.
AWS Transit Gateway simplifies and scales connectivity between multiple VPCs and on-premises networks, providing centralized routing and easier management as the number of VPCs grows.
Amazon Route 53 is a DNS service, useful for routing internet traffic, but it does not connect on-premises networks with VPCs in a hybrid cloud setup.
AWS Secrets Manager manages secrets like API keys and passwords, but it does not provide network connectivity or scaling capabilities for a hybrid cloud architecture.
I surmise that the answer is:
AWS Transit Gateway