feat: dynamic app version sourced from root VERSION file

Replaces the hardcoded version string in SettingsPage.tsx with a single
source of truth: a /VERSION file at the repo root. To cut a new release,
edit only that one file.

Frontend:
- vite.config.ts reads /VERSION at dev-server startup and injects it as
  the __APP_VERSION__ global via Vite's define mechanism (compile-time,
  zero runtime cost). Falls back to VITE_APP_VERSION env var for prod
  Docker builds that pass it as a build arg.
- vite-env.d.ts adds the TypeScript declaration for __APP_VERSION__.
- SettingsPage.tsx Badge now renders {__APP_VERSION__} instead of the
  literal string.

Backend:
- app.controller.ts reads /VERSION once at module load and includes
  "version" in both GET /api and GET /api/health responses.
- NewRelicTransactionInterceptor tags every NR transaction with
  newrelic.addCustomAttribute('appVersion', version) so releases can be
  compared in NRQL: SELECT average(duration) FROM Transaction WHERE
  appVersion = '2026.5.22'

Docker:
- docker-compose.yml mounts ./VERSION:/app/VERSION:ro in both backend
  and frontend dev containers.
- Production Dockerfiles include COPY VERSION ./ with a comment
  instructing CI to copy the root VERSION into each build context before
  docker build.

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

backend/Dockerfile

@@ -7,6 +7,9 @@ WORKDIR /app
 COPY package*.json ./
 RUN npm ci
 COPY . .
+# VERSION must be copied into the build context before `docker build`.
+# In CI / deploy scripts run: cp VERSION backend/VERSION  (or pass --build-arg)
+COPY VERSION ./
 RUN npm run build
 
 # Stage 2: Production
@@ -17,9 +20,10 @@ WORKDIR /app
 COPY package*.json ./
 RUN npm ci --omit=dev && npm cache clean --force
 
-# Copy compiled output and New Relic preload from builder
+# Copy compiled output, New Relic preload, and VERSION from builder
 COPY --from=builder /app/dist ./dist
 COPY --from=builder /app/newrelic-preload.js ./newrelic-preload.js
+COPY --from=builder /app/VERSION ./VERSION
 
 # New Relic agent — configured entirely via environment variables
 ENV NEW_RELIC_NO_CONFIG_FILE=true