This removes all the relevant code from the component, and significantly
rewrites the component specs, since they weren't written in a way that
made it easy to simply remove contexts/tests.

The removed code was added in
https://gitlab.com/gitlab-org/gitlab/-/merge_requests/48769, and the
feature flag was enabled by default in
https://gitlab.com/gitlab-org/gitlab/-/merge_requests/49572.

Addresses https://gitlab.com/gitlab-org/gitlab/-/issues/292266.