campaigns: use the user token for gitserver

Created by: LawnGnome

From @mrnugget:

After writing this comment in the draft PR (https://github.com/sourcegraph/sourcegraph/pull/15301#discussion_r516574445) I realised that "pushing commits" here was added after I called it out in this comment last week https://docs.google.com/document/d/1AM37p6WoHh01R403BYnqguQQgeXEaBYEvd6s_ldTOAA/edit?disco=AAAAKm-zxOI

Now I'm wondering: was "pushing commits" even considered in the technical conception of "user tokens"?

As far as I know (please confirm this, Adam): GitHub access tokens can be used to push commits. But what about Bitbucket Server tokens? GitLab?

I assumed that this — pushing commits — is what we all included when we talked about "code host interactions".