There are liveness and readiness probes defined on the envoy-gateway Deployment: https://github.com/envoyproxy/gateway/blob/main/internal/provider/kubernetes/config/envoy-gateway/deploy_and_ns.yaml#L40-L49
However, I don't see any code that implements these, and in my test cluster the pod is not responding to them and therefore not becoming ready / getting restarted regularly.
They need to either be implemented, or removed for now until we're ready to implement them so the pod can at least run.