Should I separate my Terraform configuration into two repositories, one as a stand-alone module that I could open source with the core configuration, and another repo with the backend config? I want to be able to open source my Terraform configuration but not hard code Terraform Cloud as the backend. I also want to be able to develop this using Terraform Cloud with GitHub. I am not sure there is a way to trigger a workspace run when I push a commit to a private module.
There is insufficient information here to offer advice. Unless your particular Terraform provider is especially complicated, it usually suffices to just document the resources, including a few examples - there is no need to release a module.
I’ve seen modules which are just thin wrappers over existing functionality in their relevant provider, which don’t really provide value - just another layer of abstraction. You would need to share specifics about the provider and proposed modules, for people to give a more useful response.