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/apps/daemon_set.go

@@ -513,7 +513,7 @@ var _ = SIGDescribe("Daemon set [Serial]", func() {
 		}
 		// delay shutdown by 15s to allow containers to overlap in time
 		ds.Spec.Template.Spec.Containers[0].Lifecycle = &v1.Lifecycle{
-			PreStop: &v1.Handler{
+			PreStop: &v1.LifecycleHandler{
 				Exec: &v1.ExecAction{
 					Command: []string{"/bin/sh", "-c", "sleep 15"},
 				},
@@ -521,7 +521,7 @@ var _ = SIGDescribe("Daemon set [Serial]", func() {
 		}
 		// use a readiness probe that can be forced to fail (by changing the contents of /var/tmp/ready)
 		ds.Spec.Template.Spec.Containers[0].ReadinessProbe = &v1.Probe{
-			Handler: v1.Handler{
+			ProbeHandler: v1.ProbeHandler{
 				Exec: &v1.ExecAction{
 					Command: []string{"/bin/sh", "-ec", `touch /var/tmp/ready; [[ "$( cat /var/tmp/ready )" == "" ]]`},
 				},