Manage sidekiq-cluster through bin/background_jobs

We're looking forward to default to using sidekiq-cluster instead sidekiq, though currently bin/background_jobs starts bundle exec sidekiq directly at:

1. GDK though bin/background_jobs start_foreground
2. Source installations through bin/background_jobs restart

Proposal

1. Rollout bin/background_jobs start_foreground changes for starting sidekiq-cluster (through ENV var or direct sidekiq-cluster call - I'm leaning towards the former considering it'd be good to have a way to disable sidekiq-cluster if something isn't right locally).
2. Make sure Source installations won't receive this change when emitting bin/background_jobs restart
3. As a follow-up, after releasing this for GDK and Core, we could move towards Source installations.

Note: Important to consider that all commands will need to work for the sidekiq-cluster (e.g. restart).

Old description.

From gitlab-org/gitlab#34396 (closed):

Deprecate or rewrite/remove `bin/background_jobs` in favor of `ee/bin/sidekiq-cluster`. Perhaps for now it could simply forward to or alias `sidekiq-cluster`.