fix: use multi-stage Docker build for backend compilation

TypeScript is a devDependency, so npx tsc failed when installed
with --omit=dev. Now using a dedicated backend-build stage that
installs all deps, compiles TS, then only the dist/ output is
copied into the final production image.

Made-with: Cursor

Dockerfile

@@ -1,3 +1,4 @@
+# --- Stage 1: Build frontend ---
 FROM node:20-slim AS frontend-build
 
 WORKDIR /app/frontend
@@ -6,6 +7,16 @@ RUN npm install
 COPY frontend/ ./
 RUN npm run build
 
+# --- Stage 2: Build backend ---
+FROM node:20-slim AS backend-build
+
+WORKDIR /app
+COPY backend/package.json backend/package-lock.json* ./
+RUN npm install
+COPY backend/ ./
+RUN npx tsc
+
+# --- Stage 3: Production image ---
 FROM node:20-slim
 
 RUN apt-get update && apt-get install -y --no-install-recommends \
@@ -33,15 +44,16 @@ RUN apt-get update && apt-get install -y --no-install-recommends \
     && rm -rf /var/lib/apt/lists/*
 
 WORKDIR /app
+
+# Copy compiled backend + prod dependencies
 COPY backend/package.json backend/package-lock.json* ./
 RUN npm install --omit=dev
+COPY --from=backend-build /app/dist ./dist
 
-# Install Playwright Chromium (optional, controlled by ENABLE_PDF)
+# Install Playwright Chromium
 RUN npx playwright install chromium || echo "Playwright install skipped"
 
-COPY backend/ ./
-RUN npx tsc
-
+# Copy frontend build
 COPY --from=frontend-build /app/frontend/dist ./frontend-dist
 
 # Copy CSS source files for the HTML renderer