core: replace logbuffer with logtree

Test Plan: Component logs are currently untested?

X-Origin-Diff: phab/D643
GitOrigin-RevId: 44ace0a1937aee9ba6a49db6e862907ec24d6ea3
diff --git a/core/internal/kubernetes/kubelet.go b/core/internal/kubernetes/kubelet.go
index d45a238..7a80f60 100644
--- a/core/internal/kubernetes/kubelet.go
+++ b/core/internal/kubernetes/kubelet.go
@@ -141,11 +141,5 @@
 		fmt.Sprintf("--root-dir=%s", s.KubeletDirectory.FullPath()),
 	)
 	cmd.Env = []string{"PATH=/kubernetes/bin"}
-	cmd.Stdout = s.Output
-	cmd.Stderr = s.Output
-
-	supervisor.Signal(ctx, supervisor.SignalHealthy)
-	err = cmd.Run()
-	fmt.Fprintf(s.Output, "kubelet stopped: %v\n", err)
-	return err
+	return supervisor.RunCommand(ctx, cmd)
 }