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You can put hooks on the server side of git. It can do pretty much anything that CI/CD can.

That requires Github Enterprise (if using GH, of course), no?

Well it requires a server and 5 minutes of your time :) I guess you can always have it as a mirror for your GH repository. Gitlab has push mirroring, not sure about GH: https://docs.gitlab.com/user/project/repository/mirror/push/