In EE, the DeployKeyController reloads the user's accesible key so that
it can audit changes. However, this has a side effect of preventing
admins from deleting keys in the interface.  Note that the deletion
problem does not happen in CE because auditing is not performed there.

We can clean up the code by reusing the key that was created or destroyed
and pushing the logic into the service.

Closes https://gitlab.com/gitlab-org/gitlab-ce/issues/53783