urlbased loadbalancing of websocketconnections in Kubernetes with Ingress

I think in this case you can look into the Envoy and Istio direction.

You might be interested in LoadBalancerSettings.ConsistentHashLB flag:

Consistent Hash-based load balancing can be used to provide soft session affinity based on HTTP headers, cookies or other properties. This load balancing policy is applicable only for HTTP connections. The affinity to a particular destination host will be lost when one or more hosts are added/removed from the destination service.

From Envoy Supported load balancers - ring-hash documentation

The ring/modulo hash load balancer implements consistent hashing to upstream hosts. Each host is mapped onto a circle (the “ring”) by hashing its address; each request is then routed to a host by hashing some property of the request, and finding the nearest corresponding host clockwise around the ring. This technique is also commonly known as “Ketama” hashing, and like all hash-based load balancers, it is only effective when protocol routing is used that specifies a value to hash on.

Each host is hashed and placed on the ring some number of times proportional to its weight. For example, if host A has a weight of 1 and host B has a weight of 2, then there might be three entries on the ring: one for host A and two for host B. This doesn’t actually provide the desired 2:1 partitioning of the circle, however, since the computed hashes could be coincidentally very close to one another; so it is necessary to multiply the number of hashes per host—for example inserting 100 entries on the ring for host A and 200 entries for host B—to better approximate the desired distribution. Best practice is to explicitly set minimum_ring_size and maximum_ring_size, and monitor the min_hashes_per_host and max_hashes_per_host gauges to ensure good distribution. With the ring partitioned appropriately, the addition or removal of one host from a set of N hosts will affect only 1/N requests.

When priority based load balancing is in use, the priority level is also chosen by hash, so the endpoint selected will still be consistent when the set of backends is stable.