De-share the Handler struct in core API (#105979)

* De-share the Handler struct in core API

An upcoming PR adds a handler that only applies on one of these paths.
Having fields that don't work seems bad.

This never should have been shared.  Lifecycle hooks are like a "write"
while probes are more like a "read". HTTPGet and TCPSocket don't really
make sense as lifecycle hooks (but I can't take that back). When we add
gRPC, it is EXPLICITLY a health check (defined by gRPC) not an arbitrary
RPC - so a probe makes sense but a hook does not.

In the future I can also see adding lifecycle hooks that don't make
sense as probes.  E.g. 'sleep' is a common lifecycle request. The only
option is `exec`, which requires having a sleep binary in your image.

* Run update scripts

test/e2e/framework/network/utils.go

@@ -558,7 +558,7 @@ func (config *NetworkingTestConfig) createNetShellPodSpec(podName, hostname stri
 		PeriodSeconds:       10,
 		SuccessThreshold:    1,
 		FailureThreshold:    3,
-		Handler: v1.Handler{
+		ProbeHandler: v1.ProbeHandler{
 			HTTPGet: &v1.HTTPGetAction{
 				Path: "/healthz",
 				Port: intstr.IntOrString{IntVal: EndpointHTTPPort},

test/e2e/framework/service/jig.go

@@ -646,7 +646,7 @@ func (j *TestJig) newRCTemplate() *v1.ReplicationController {
 							Args:  []string{"netexec", "--http-port=80", "--udp-port=80"},
 							ReadinessProbe: &v1.Probe{
 								PeriodSeconds: 3,
-								Handler: v1.Handler{
+								ProbeHandler: v1.ProbeHandler{
 									HTTPGet: &v1.HTTPGetAction{
 										Port: intstr.FromInt(80),
 										Path: "/hostName",

test/e2e/framework/statefulset/fixtures.go

@@ -117,7 +117,7 @@ func hasPauseProbe(pod *v1.Pod) bool {
 }
 
 var pauseProbe = &v1.Probe{
-	Handler: v1.Handler{
+	ProbeHandler: v1.ProbeHandler{
 		Exec: &v1.ExecAction{Command: []string{"test", "-f", "/data/statefulset-continue"}},
 	},
 	PeriodSeconds:    1,