HAProxy config rewrite: Identify currently used features and traffic paths

This issue is the first cornerstone to see what we are using in HAProxy right now, what we should keep, what we should rework and what we should just yeet.

The results will not be added in this description, but in this internal note: https://gitlab.com/gitlab-com/gl-infra/reliability/-/issues/16845#note_1180129618

Acceptance Criteria:

• We have a flowchart (or equivalent) of how requests are routed right now
• All features to retain in rewrites or use in alternate solutions are documented