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/node/pre_stop.go

@@ -77,7 +77,7 @@ func testPreStop(c clientset.Interface, ns string) {
 					Image:   imageutils.GetE2EImage(imageutils.BusyBox),
 					Command: []string{"sleep", "600"},
 					Lifecycle: &v1.Lifecycle{
-						PreStop: &v1.Handler{
+						PreStop: &v1.LifecycleHandler{
 							Exec: &v1.ExecAction{
 								Command: []string{
 									"wget", "-O-", "--post-data=" + val, fmt.Sprintf("http://%s/write", podURL),
@@ -225,7 +225,7 @@ func getPodWithpreStopLifeCycle(name string) *v1.Pod {
 					Name:  "nginx",
 					Image: imageutils.GetE2EImage(imageutils.Nginx),
 					Lifecycle: &v1.Lifecycle{
-						PreStop: &v1.Handler{
+						PreStop: &v1.LifecycleHandler{
 							Exec: &v1.ExecAction{
 								Command: []string{"sh", "-c", "while true; do echo preStop; sleep 1; done"},
 							},