[serve] Use ray.experimental.metrics (#10185)

python/ray/serve/BUILD

@@ -64,15 +64,6 @@ py_test(
 )
 
 
-py_test(
-    name = "test_metric",
-    size = "small",
-    srcs = serve_tests_srcs,
-    tags = ["exclusive"],
-    deps = [":serve_lib"],
-)
-
-
 py_test(
     name = "test_persistence",
     size = "small",
@@ -201,14 +192,6 @@ py_test(
     deps = [":serve_lib"]
 )
 
-py_test(
-    name = "snippet_metric_export",
-    size = "small",
-    srcs = glob(["examples/doc/*.py"]),
-    tags = ["exclusive"],
-    deps = [":serve_lib"]
-)
-
 # Disable the deployment tutorial test because it requires
 # ray start --head in the background.
 # py_test(