The "path" part of the endpoint URLs themselves (for this SO question, the /questions/53008947/... part) won't change. But the rest of the URL might.

Docker publishes services at a TCP-port level (docker run -p option, Docker Compose ports: section) and doesn't look at what traffic is going over a port. If you have something like an Apache or nginx proxy as part of your stack that might change the HTTP-level path mappings, but you'd probably be aware of that in your environment.

Kubernetes works similarly, but there are more layers. A container runs in a Pod, and can publish some port out of the Pod. That's not used directly; instead, a Service refers to the Pod (by its labels) and republishes its ports, possibly on different port numbers. The Service has a DNS name service-name.namespace.svc.cluster.local that can be used within the cluster; you can also configure the Service to be reachable on a fixed TCP port on every node in the service (NodePort) or, if your Kubernetes is running on a public-cloud provider, to create a load balancer there (LoadBalancer). Again, all of this is strictly at the TCP level and doesn't affect HTTP paths.

There is one other Kubernetes piece, an Ingress controller, which acts as a declarative wrapper around the nginx proxy (or something else with similar functionality). That does operate at the HTTP level and could change paths.

The other corollary to this is that the URL to reach a service might be different in different environments: http://localhost:12345/path in a local development setup, http://other_service:8080/path in Docker Compose, http://other-service/path in Kubernetes, https://api.example.com/other/path in production. You need some way to make that configurable (often an environment variable).