Hi Meet,
Glad you found this useful :)
Great question! tl;dr: The choice of an STS region doesn't actually limit Vault to only working with clients that specific region. It will work with clients in any AWS region in the same "partition" (the AWS partitions are Standard, GovCloud, and AWS China). So, I would recommend having all clients just use the region your Vault server is in, which in your use case is us-east-1.
A longer explanation:
With regards to regions, STS is a weird and confusing AWS service. It's global in the sense that credentials issued by IAM and STS are valid in any AWS region (in the same partition), e.g., credentials issued by STS in us-west-2 are valid in us-east-1 (but wouldn't be valid in regions in GovCloud or in China). However, STS is regional in the sense that STS endpoints exist in each AWS region. This means that all of your clients in every region (within the same AWS partition) can authenticate using a single STS region configured in Vault. They just all need to know to generate login requests for the region that the Vault server uses.
The way Vault does IAM authentication, the only impact the AWS region has on Vault clients is on the content of the login request sent to the Vault server. In the Vault IAM authentication login flow, the client doesn't communicate with STS at all. Rather, the Vault server is what communicates with STS. So, to minimize network latency, I would recommend choosing the STS region that is closest to your Vault server. In the example you gave, your Vault clients in us-west-2 would use their credentials to generate a Vault login request, send that to the Vault server in us-east-1, and then the Vault server would send that to STS in us-east-1, which would then respond to your Vault server and that would respond back to your clients. That's only a single hop across the US. If you chose an STS region of us-west-2 for your Vault server in us-east-1, then your clients in us-west-2 would send the login request to your Vault server in us-east-1, which would then send the request to the STS endpoint back in us-west-2, which would respond back to Vault in us-east-1, which would respond to your client in us-west-2, resulting in two hops across the US.
If for some reason you must use STS endpoints in different regions, as Vault is currently configured today, you would need to have multiple mounts of the AWS auth method and configure the appropriate region in each.
Hope this helps!
--Joel