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/network/service.go

@@ -1684,14 +1684,14 @@ var _ = common.SIGDescribe("Services", func() {
 			Image: t.Image,
 			Ports: []v1.ContainerPort{{ContainerPort: int32(port), Protocol: v1.ProtocolTCP}},
 			ReadinessProbe: &v1.Probe{
-				Handler: v1.Handler{
+				ProbeHandler: v1.ProbeHandler{
 					Exec: &v1.ExecAction{
 						Command: []string{"/bin/false"},
 					},
 				},
 			},
 			Lifecycle: &v1.Lifecycle{
-				PreStop: &v1.Handler{
+				PreStop: &v1.LifecycleHandler{
 					Exec: &v1.ExecAction{
 						Command: []string{"/bin/sleep", fmt.Sprintf("%d", terminateSeconds)},
 					},