These pipelines do not imply moving away from Sidekiq. Have you tried using the Omnibus package? It contains logic to make sure restarting Sidekiq is automatic. How much memory does GitLab have and how many users?
From https://about.gitlab.com/installation/ "One-click installers are frequently out of date and might not contain our Omnibus packages. An example of this are the Bitnami packages in the past couldn't be updated and are now much harder to update than the Omnibus packages. We advise to not use one-click installers but instead start an vanilla Ubuntu instance and use the recommended Omnibus package installation. This is almost as quick as a one-click install and you're sure of the latest version and easy upgrades."