How to configure DNS settings to effectively direct traffic between the two apps - same domain (path)

I am currently managing a domain (e.g., where the main site is hosted on WordPress and I’m in the process of incrementally transitioning to a Next.js app hosted on Vercel. I would like to use Cloudflare for DNS management and traffic routing during this transition. Could you provide guidance on the best practices for using Cloudflare in this scenario? Specifically, I am interested in how to configure DNS settings and Page Rules in Cloudflare to effectively direct traffic between the WordPress and Next.js parts of the site, especially considering options like subdomain strategy versus path-based routing. Additionally, any insights on leveraging Cloudflare’s CDN and security features during this transition would be highly appreciated.