Serve old and new API versions under the same hostname and TLS while keeping both deployable. How should you route traffic?

Using separate backend services (backend pools) per API path behind a single load balancer allows routing traffic for different API versions (e.g., /v1 and /v2) to distinct sets of backend instances. This approach enables both versions to be deployed simultaneously under the same hostname and TLS certificate, fulfilling the requirements. The load balancer's URL maps can direct requests based on the URL path to the appropriate backend service. Configuring a new load balancer for each version adds unnecessary complexity and cost. Reconfiguring legacy clients is often impractical and defeats the purpose of serving both versions under the same hostname. Having the old API forward requests to the new API introduces an additional hop, increasing latency and coupling the deployments.