www-gitlab-com manual deploy-staging CI job

Can we change the deploy-staging job to be run manually? Thus making deploys to our staging server (https://about.staging.gitlab.com) initiated manually by a user through a merge-request.

This is more immediately relevant, because it simplifies !56889 (merged), which @cwoolley-gitlab is currently working on.

This work is also going to resolve #7661 (closed)