Make MLFlow version detection more robust and handles mlflow-skinny (#29957)

* Make MLFlow version detection more robust and handles mlflow-skinny

* Make function name more clear and refactor the logic

* Further refactor

src/transformers/integrations/integration_utils.py

@@ -131,13 +131,6 @@ def is_mlflow_available():
     return importlib.util.find_spec("mlflow") is not None
 
 
-def get_mlflow_version():
-    try:
-        return importlib.metadata.version("mlflow")
-    except importlib.metadata.PackageNotFoundError:
-        return importlib.metadata.version("mlflow-skinny")
-
-
 def is_dagshub_available():
     return None not in [importlib.util.find_spec("dagshub"), importlib.util.find_spec("mlflow")]
 
@@ -1005,12 +998,12 @@ class MLflowCallback(TrainerCallback):
         self._experiment_name = os.getenv("MLFLOW_EXPERIMENT_NAME", None)
         self._flatten_params = os.getenv("MLFLOW_FLATTEN_PARAMS", "FALSE").upper() in ENV_VARS_TRUE_VALUES
         self._run_id = os.getenv("MLFLOW_RUN_ID", None)
-        self._async_log = False
+
         # "synchronous" flag is only available with mlflow version >= 2.8.0
         # https://github.com/mlflow/mlflow/pull/9705
         # https://github.com/mlflow/mlflow/releases/tag/v2.8.0
-        if packaging.version.parse(get_mlflow_version()) >= packaging.version.parse("2.8.0"):
-            self._async_log = True
+        self._async_log = packaging.version.parse(self._ml_flow.__version__) >= packaging.version.parse("2.8.0")
+
         logger.debug(
             f"MLflow experiment_name={self._experiment_name}, run_name={args.run_name}, nested={self._nested_run},"
             f" tags={self._nested_run}, tracking_uri={self._tracking_uri}"