What should a solutions architect implement to meet these requirements with the LEAST amount of operational overhead?

Explanations:

Creating a DX connection in each new account would lead to increased operational overhead and management complexity, as each account would require its own DX connection. This approach is not cost-effective and does not provide a centralized management solution.

Configuring VPC endpoints in the DX VPC would not directly facilitate routing network traffic to on-premises servers, as VPC endpoints are used to connect to AWS services privately without going through the internet. This option does not address the requirement for on-premises service access.

Establishing a VPN connection between each new account and the DX VPC would also result in increased operational overhead. Each account would require individual VPN configurations and maintenance, making this approach less scalable and more complex.

Implementing an AWS Transit Gateway provides a centralized hub for connecting multiple accounts and VPCs. By associating the DX connection with the transit gateway, all connected accounts can efficiently route traffic to the on-premises network services without the need for individual DX connections or VPNs, thus minimizing operational overhead and simplifying management.