Thats a very specific property of git, stemming from its distributed nature. Allowing one to push the history of a repo fetched from elsewhere.
The receiver of the push is still considered an application server in this case. Whether or not GitHub solves this with a proxy or by reimplementing the git protocol and solve it in process is an internal detail on their end. GitHub is still “the application”. Other git forges do this type of auth in the same process without any proxies, Gitlab or Gerrit for example, open source and self hosted, making this easy to confirm.
In fact, for such a hypothetical proxy to be able to solve this scenario, the proxy must have an implementation of git itself. How else would it know how to extract the commiter email and cross check that it matches the logged in users email?
An application almost always has the best view of what a resource is, the permissions set on it and it almost always has awareness of “who” is acting upon said resource.