Production Containerization — multi-stage Dockerfiles for backend + frontend

**Technology:** Multi-stage `Dockerfile`s (backend + frontend)

Production-grade multi-stage Docker builds for backend and frontend, with `make` targets and CI updated to build/run via Docker instead of host toolchains.

**Open question:** whether `mise`-managed toolchains are still needed inside the image or can be dropped for a leaner runtime stage.

Feeds directly into the Deployment Target feature pack (`README.md`), which selects the deploy target on top of these images. Ship in that order — the pack needs the images to exist first.

**Priority:** 5th in the Core Foundations order — production readiness, sequenced last.

Start with README.md and the backend/frontend build entry points, then map the Dockerfiles, make targets, and CI changes required by the deployment sequence. Resolve whether mise-managed toolchains remain in the image, and consider the work done when both production images build and run through Docker and the deployment pack can consume them.

Written by the indexing model from the issue text.