Log additional test metrics with the CometCallback (huggingface#33124)

* Log additional test metrics with the CometCallback.

Also follow the same metric naming convention as other callbacks

* Merge 2 subsequent if-statements

* Trigger Build

---------

Co-authored-by: Aliaksandr Kuzmik <alexander.kuzmik99@gmail.com>

src/transformers/integrations/integration_utils.py

@@ -1107,8 +1107,9 @@ def on_log(self, args, state, control, model=None, logs=None, **kwargs):
             self.setup(args, state, model)
         if state.is_world_process_zero:
             if self._experiment is not None:
+                rewritten_logs = rewrite_logs(logs)
                 self._experiment.__internal_api__log_metrics__(
-                    logs, step=state.global_step, epoch=state.epoch, framework="transformers"
+                    rewritten_logs, step=state.global_step, epoch=state.epoch, framework="transformers"
                 )
 
     def on_train_end(self, args, state, control, **kwargs):
@@ -1125,6 +1126,15 @@ def on_train_end(self, args, state, control, **kwargs):
                 self._experiment.clean()
                 self._initialized = False
 
+    def on_predict(self, args, state, control, metrics, **kwargs):
+        if not self._initialized:
+            self.setup(args, state, model=None)
+        if state.is_world_process_zero and self._experiment is not None:
+            rewritten_metrics = rewrite_logs(metrics)
+            self._experiment.__internal_api__log_metrics__(
+                rewritten_metrics, step=state.global_step, epoch=state.epoch, framework="transformers"
+            )
+
 
 class AzureMLCallback(TrainerCallback):
     """