T-2: add multi-stage Dockerfile and SPA-serving Spring Boot config

Replace server.servlet.context-path=/api with addPathPrefix so API
endpoints stay under /api while static resources and SPA routes are
served at /. Spring Boot falls back to index.html for unknown paths
(SPA forwarding). Multi-stage Dockerfile builds frontend (Node 24)
and backend (Temurin 25) into a single 250MB JRE-alpine image with
Docker-native HEALTHCHECK.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

spec/setup-tasks.md

@@ -26,11 +26,11 @@
 **Description:** Create a multi-stage Dockerfile that builds backend and frontend and produces a single runnable container. This task focuses exclusively on the Docker build — database wiring, environment variable configuration, and docker-compose documentation are deferred to T-4 (where JPA and migration tooling are introduced).
 
 **Acceptance Criteria:**
-- [ ] Single multi-stage Dockerfile at repo root that builds backend and frontend and produces one container
-- [ ] `.dockerignore` excludes build artifacts, IDE files, and unnecessary files from the build context
+- [x] Single multi-stage Dockerfile at repo root that builds backend and frontend and produces one container
+- [x] `.dockerignore` excludes build artifacts, IDE files, and unnecessary files from the build context
 - [x] Health-check endpoint so Docker/orchestrators can verify the app is alive
-- [ ] `docker build .` succeeds and produces a working image
-- [ ] Container starts and the health-check endpoint responds
+- [x] `docker build .` succeeds and produces a working image
+- [x] Container starts and the health-check endpoint responds
 
 **Dependencies:** T-1, T-5