Move all process related methods to the ProcessManagement module

What does this MR do and why?

This MR moves process-related methods from sidekiq_cluster.rb to its own module process_management.rb. It does not change any functionality.

In this PoC !73049 (closed) we noticed that we will re-use certain process-related methods previously defined in sidekiq_cluster.rb. Moving the methods to their own module keeps the code dry.

This MR is a step in creating a Sidekiq metrics server &6409 (closed)

How to set up and validate locally

Numbered steps to set up and validate the change are strongly suggested.

1. Run bin/background_jobs (GDK does this when you run gdk start)
2. curl localhost:<metrics_port>/metrics -- it should serve metrics. Default metrics port is 3807

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this MR.

Related to #345880 (closed)