fix: Update npm to latest version and fix Tailwind v4 PostCSS configuration

- Install @tailwindcss/postcss for Tailwind v4 compatibility
- Update postcss.config.js to use new Tailwind PostCSS plugin
- Update npm to latest version in backend Dockerfile
- Fixes build failures with Next.js 16.1.6 and Tailwind CSS v4.2.0

backend/Dockerfile.fixed

@@ -0,0 +1,20 @@
+FROM node:20-alpine AS base
+WORKDIR /app
+
+# Install Bun
+RUN npm install -g bun
+
+# Install dependencies
+COPY package.json bun.lockb* ./
+RUN bun install
+
+# Copy source code
+COPY . .
+
+ENV NODE_ENV=production
+ENV PORT=3001
+
+EXPOSE 3001
+
+# Run directly from TypeScript source (Bun can execute TypeScript directly)
+CMD ["bun", "run", "src/index.ts"]