The root module can have outputs just like any other module. These outputs can be accessed from other stacks from the backend.
And if you use CDKTF the references are handled transparently.
It is reasonable to assume if you are using Terraform to manage your infra, than your infra likely has access to a secrets manager from your infra vendor, e.g., AWS. Instead I'd recommend using a Terraform data resource to pull a credential from the secret manager by name -- and the name doesn't even necessarily have to be communicated through Terraform state. Then the credentials could directly be fed into where it is needed, e.g., a resource like a Kubernetes Secret. One can even skip this whole thing if the service can use the secret manager api itself. Finally access to the credentials itself would be locked down with IAM/RBAC.