build: Docker setup (compose: postgres + all-in-one api image)

- Dockerfile: 3-stage — Flutter web build, NestJS build, slim node runtime.
  Runtime copies dist + node_modules + prisma + the web bundle
  (WEB_CLIENT_DIR=/app/web), runs `prisma migrate deploy` then `node
  dist/main.js`. One container serves client + API on :3000.
- docker-compose.yml: postgres:16-alpine with a healthcheck + the api
  service; config from backend/.env (Compose v2 strips quotes),
  DATABASE_URL + GOOGLE_APPLICATION_CREDENTIALS overridden for the
  container, serviceAccount.json bind-mounted read-only.
- .dockerignore keeps node_modules/build/secrets out of the context.

Not run here (no Docker on this box); the stack also runs natively against
the local Postgres.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

.dockerignore

@@ -0,0 +1,10 @@
+**/node_modules
+**/dist
+**/build
+**/.dart_tool
+**/coverage
+.git
+**/*.log
+# Secrets: passed at runtime via env_file / bind mount, never baked in.
+backend/.env
+backend/serviceAccount.json