In addition to Transit Gateway, there's also AWS PrivateLink [1], which is my preferred approach for scenarios where it works. As an alternative to peering entire networks together, PrivateLink allows you to establish minimal connectivity between specific clients and services that need to communicate. When a service supports PrivateLink, any authorized client can create a private endpoint for that service in their VPC, and the endpoint receives a local IP address (in that VPC).
This has a couple of benefits. The first is that you don't need to coordinate IP address ranges in different VPCs, which is necessary if you're peering them together (unless you're using NAT). IPv4 address management in large networks can be challenging.
The second benefit is that although clients can communicate with the service, there isn't an actual route between the two networks. This better achieves the principle of least privilege at the network level; it avoids the security risks of connecting networks together such that any machine can connect to any other. When you design an application network to use PrivateLink from the ground up, you can start with the expectation that the VPC doesn't need any connections to any other networks, not even the Internet; it can potentially be an isolated network bubble, with only PrivateLinks allowing traffic in and out (using e.g. Session Manager for administration).
There are also practical limits on how large a federated network of peered VPCs can grow (probably helped by Transit Gateway), but there isn't any limit I'm aware of on the number of client/server connections that can be established with PrivateLink.
For these reasons I prefer to use PrivateLink when building systems that communicate across VPCs, falling back to network peering or Internet-facing endpoints in scenarios where it doesn't work.
However, one downside compared to network peering is that you need to set up a PrivateLink connection for each service that each client needs to call, though this process can be automated during infrastructure provisioning. Services need to have specifically onboarded with PrivateLink; you can't just deploy a service on the network and have it work.
[1] https://aws.amazon.com/privatelink/