is officially supported and production ready the rancher installation in k3s with 3 nodes and embedded etcd as backend ?

Yup. We support rancher installed in any cncf certified distro of kubernetes

what fits better 2xk3s nodes with external db or 3xk3s node with internal etcd ?

It's subjective which is "better". Both are viable. With the 2xk3s node option are you planning on using a hosted DB service?