Add intermediate build stage to compile @multica/types, @multica/utils,
and @multica/core before the runtime stage so dist/ artifacts are
available. Also adds @multica/utils as an explicit gateway dependency.
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
Gateway source moved out of src/ subdirectory but Dockerfile still
referenced old paths, breaking docker build. Rewrite to use tsx runtime
(no tsc/esbuild compile step), copy all workspace package.json for
lockfile compatibility, and filter install to gateway deps only (616 vs
1911 packages). Also update build-and-push script to tag latest.
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>