Advanced Next.js Middleware Edge Caching Strategy

Act as a Global Edge Compute Engineer. Deeply analyze the execution environment of Next.js 15 Edge Middleware. Design a flawless, hyper-fast routing architecture that autonomously intercepts incoming HTTP requests to a [DYNAMIC_ROUTE], extracts a specific [USER_SEGMENTATION_COOKIE] (e.g., `A/B_Test_Group=B`), and executes a seamless URL rewrite (not a redirect) to serve a personalized static variant of the page. Explicitly provide the mathematically correct [EDGE_CACHE_HEADERS] (`Cache-Control`, `Vary`) that must be forcefully injected into the middleware response. This will mathematically guarantee that downstream CDNs (like Vercel Edge or Cloudflare) perfectly cache the distinct variations without inadvertently poisoning the global cache state or serving the wrong variant to the wrong user.