👋 Is there a doc that shows how to use pulumi to create a Hashicorp Vault server from scratch on AWS?

Unfortunately, I don't know of one. There are a couple rough examples we use to test the provider builds in https://github.com/pulumi/pulumi-vault, and there's the configuration details in https://www.pulumi.com/registry/packages/vault/installation-configuration/, but nothing like what you're looking for.