matthyx: Automated cherry pick of #98571: Stop probing a pod during graceful shutdown

JobBuild
c294831d
03-24 14:30
100527
03-24 14:30
pull-kubernetes-bazel-build 1374729791818698752
pull-kubernetes-bazel-test 1374729791848058880
pull-kubernetes-dependencies 1374729791877419008
pull-kubernetes-e2e-gce 1374729791751589888
pull-kubernetes-e2e-gce-100-performance 1374729791801921536
pull-kubernetes-e2e-kind 1374729791923556352
pull-kubernetes-integration 1374729791890001920
pull-kubernetes-node-e2e 1374729791772561408
pull-kubernetes-typecheck 1374729791948722176
pull-kubernetes-verify 1374729791952916480