I ran into the same issue when trying to create a pipeline for a private repository under a GitHub organization. The error I received was:

"Unable to configure a service on the selected GitHub repository. This is likely caused by not having the necessary permission to manage hooks for the selected repository."

In our case, the issue was due to missing GitHub App permissions. We resolved it by going to the GitHub organization settings, adding Azure DevOps under GitHub Apps, and explicitly granting access to the repositories we wanted to use in Azure DevOps.

Important: Only a GitHub organization admin or a user with admin access to the repository can make these permission changes. If you don’t have that level of access, you’ll need to request it or ask someone with the necessary rights to configure it for you.

Once the permissions were set correctly, Azure DevOps was able to configure the required webhooks, and the pipeline setup worked smoothly.

Hope this helps someone facing the same issue!