Which set of additional steps should the solutions architect take to meet these requirements?

Explanations:

Creating peering connections between the egress VPC and the spoke VPCs would require managing multiple peering connections as the number of spoke VPCs increases, making this approach cumbersome and less scalable. Additionally, peering connections do not automatically enable transit routing or share a single NAT gateway, which is needed for efficient internet access from multiple spokes.

A transit gateway provides a scalable way to connect multiple VPCs across different accounts. By creating a transit gateway and sharing it with the existing AWS accounts, the solutions architect can attach the spoke VPCs to this central hub. The transit gateway simplifies routing and allows all private subnets in the spoke VPCs to route internet-bound traffic through the NAT gateway in the egress VPC efficiently.

Creating a transit gateway in every account adds unnecessary complexity and overhead. This design does not leverage the benefits of a centralized transit gateway, resulting in more complicated routing configurations and NAT gateway management across multiple accounts. The NAT gateway would not be shared effectively across all spoke VPCs.

AWS PrivateLink is designed for providing secure access to services hosted in one VPC from another VPC without exposing them to the public internet. It does not facilitate internet access from private subnets. This approach would not meet the requirement of routing internet traffic through a central NAT gateway, as PrivateLink does not route traffic to the internet.