Github integration today only works for regular Github and Github Enterprise Cloud, both residing on github.com, but does not seem to support the Github Enterprise Cloud with Data Residency, which host instances on separate subdomains under ghe.com, like example.ghe.com (or github.ghe.com which seems to be an actual instance).

Besides from that, connecting third party integrations should not be an issue, but there is unfortunately nowhere I can tell the Github integration which server to use.