Using the Terraform VCS Oauth Client to manage Github

I’m relatively new to Terraform, and I checked around for a topic like this and I cannot quite find one. Its entirely possible I have overlooked a very simple fix for the below.

I am trying to model out how to manage our GitHub environment with Terraform Cloud. Starting with a Seed repository that will be manually configured in both GitHub and Terraform to configure our initial VCS connection. Now that I have that… I am able to kick off Terraform jobs by pushing to my repo with no problem. The problem I’m trying to solve is how to manage GitHub from Terraform Cloud.

I see there is a GitHub provider. It would like various inputs to initiate the connection back to GitHub (token or appauth). I thought that since we have an Oauth Client already configured via the VCS console… that i could use that to connect back to GitHub and leverage this to continue to manage my infrastructure.
My thought was to use a datasource for the tfe_oauth_client, but I don’t see a way to actually provide the appauth requirements as data sources/variables, nor do I see a way to pass the token.

is there a simple way within terraform cloud to leverage the oauth connection that has already been established between terraform and GitHub in order to leverage the GitHub provider and manage my GitHub infrastructure, or do I need to look at creating a separate GitHub app in order to manage that portion of my infrastructure?

thank you all for your time!