Evaluate sharing build and CICD code between coordinator and existing pipelines

[revit13]

Follow-up from PR #1975 review comment. The coordinator landed with dedicated
build/CI tooling (Makefile.coord.mk, .github/workflows/ci-coordinator.yaml) that
re-declares variables, container-runtime plumbing, and targets already defined for the
router build. This tracks investigating how much can share the existing infrastructure.

Questions to answer

1. Should coordinator CI reuse existing workflows (ci-pr-checks, ci-lint,
   ci-build-images) instead of a dedicated ci-coordinator.yaml and merge gate?
2. Is a separate Makefile.coord.mk warranted, or should its targets be inlined into the
   existing Makefiles? It duplicates defaults (TARGETOS, IMAGE_REGISTRY, builder image),
   the docker/podman socket plumbing, and targets (presubmit, format, lint,
   test-unit, image-build-%).

[revit13]

duplication of #2079