fix: permissions in with-docker example (#63134)

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### What

This pr addresses an issue in Docker where the cache and the creation of
its contents throw the following error:

```
[Error: EACCES: permission denied, mkdir '/app/.next/cache'] {
errno: -13,
code: 'EACCES',
syscall: 'mkdir',
path: '/app/.next/cache'
```

Co-authored-by: Sam Ko <sam@vercel.com>

examples/with-docker/Dockerfile

@@ -22,6 +22,8 @@ WORKDIR /app
 COPY --from=deps /app/node_modules ./node_modules
 COPY . .
 
+RUN mkdir -p public
+
 # Next.js collects completely anonymous telemetry data about general usage.
 # Learn more here: https://nextjs.org/telemetry
 # Uncomment the following line in case you want to disable telemetry during the build.
@@ -45,17 +47,17 @@ ENV NODE_ENV production
 RUN addgroup --system --gid 1001 nodejs
 RUN adduser --system --uid 1001 nextjs
 
-COPY --from=builder /app/public ./public
-
-# Set the correct permission for prerender cache
-RUN mkdir .next
-RUN chown nextjs:nodejs .next
-
 # Automatically leverage output traces to reduce image size
 # https://nextjs.org/docs/advanced-features/output-file-tracing
+COPY --from=builder --chown=nextjs:nodejs /app/public ./public
 COPY --from=builder --chown=nextjs:nodejs /app/.next/standalone ./
 COPY --from=builder --chown=nextjs:nodejs /app/.next/static ./.next/static
 
+# Set the correct permission for prerender cache
+RUN mkdir -p .next/cache
+RUN chown -R nextjs:nodejs .next
+RUN chmod -R 777 .next/cache
+
 USER nextjs
 
 EXPOSE 3000