fix(api): auto-run migrations on container start and fix ESM warning

- Add docker-entrypoint.sh that runs prisma migrate deploy before
  starting the app, ensuring all tables exist on deployment
- Add "type": "module" to package.json to eliminate Node.js ESM
  reparsing warning for eslint.config.js

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

apps/api/Dockerfile

@@ -80,6 +80,9 @@ COPY --from=builder --chown=nestjs:nodejs /app/apps/api/package.json ./apps/api/
 # Copy app's node_modules which contains symlinks to root node_modules
 COPY --from=builder --chown=nestjs:nodejs /app/apps/api/node_modules ./apps/api/node_modules
 
+# Copy entrypoint script (runs migrations before starting app)
+COPY --from=builder --chown=nestjs:nodejs /app/apps/api/docker-entrypoint.sh ./apps/api/
+
 # Set working directory to API app
 WORKDIR /app/apps/api
 
@@ -96,5 +99,5 @@ HEALTHCHECK --interval=30s --timeout=10s --start-period=40s --retries=3 \
 # Use dumb-init to handle signals properly
 ENTRYPOINT ["dumb-init", "--"]
 
-# Start the application
-CMD ["node", "dist/main.js"]
+# Run migrations then start the application
+CMD ["sh", "docker-entrypoint.sh"]