feature: Implement readyz and livez handlers for the proxy server

[ntnn]

Feature Description

Currently the proxy server only returns OK without any actual health/liveness checks:

kcp/pkg/proxy/server.go

Lines 146 to 158 in 301a8f7

	mux := http.NewServeMux()
	// TODO: implement proper readyz handler
	mux.Handle("/readyz", http.HandlerFunc(func(w http.ResponseWriter, r *http.Request) {
	w.Write([]byte("OK")) //nolint:errcheck
	}))
	// TODO: implement proper livez handler
	mux.Handle("/livez", http.HandlerFunc(func(w http.ResponseWriter, r *http.Request) {
	w.Write([]byte("OK")) //nolint:errcheck
	}))
	mux.Handle("/", handler)
	s.Handler = mux

Proposed Solution

Implement the checks.
livez could even stay as it. healthz could check the informer state with https://pkg.go.dev/k8s.io/apiserver@v0.35.2/pkg/server/healthz

Alternative Solutions

No response

Want to contribute?

• I would like to work on this issue.

Additional Context

No response

[kanhaiyagithub]

could you please assign this issues to me so that i can work on this issues

[cnvergence]

/assign nuromirg