Finally client reached out to their Github Enterprise admin to find out.

Their Enterprise Admin told us this:

Your GitHub Enterprise Server version is affected by a known issue between the webhook service and the background job queue service. Running the following commands should reset the service and resolve the problem:

nomad job stop --purge haproxy-cluster-proxy
sudo nomad job run /etc/nomad-jobs/haproxy/haproxy-cluster-proxy.hcl

Upgrading to version 3.16.9 is recommended to prevent this issue from recurring.
If these commands don’t resolve the issue, please let me know.