proxy:implement readyz and livez handlers

[nuromirg]

Summary

Replace the stub OK responses on /readyz and /livez with health checks using the recommended k8s.io/apiserver/pkg/server/healthz package from issue description.

In short,

• /readyz uses NewInformerSyncHealthz and reports ready only once the shared informer factory caches have synced
• /livez now uses PingHealthz for liveness ping (didn't find any meaningful broken-but-alive state, I assume that simple ping-pong would be fine)

What Type of PR Is This?

/kind feature

Related Issue(s)

Fixes #3916

Release Notes

NONE

[kcp-ci-bot]

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[kcp-ci-bot]

Hi @nuromirg. Thanks for your PR.

I'm waiting for a kcp-dev member to verify that this patch is reasonable to test. If it is, they should reply with /ok-to-test on its own line. Until that is done, I will not automatically test new commits in this PR, but the usual testing commands by org members will still work. Regular contributors should join the org to skip this step.

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[ntnn]

Thanks @nuromirg for the contribution!
/ok-to-test