Rewrite push_to_hub to use upload_files (#18366)

* Rewrite push_to_hub to use upload_files

* Adapt the doc a bit

* Address review comments and clean doc

docs/source/en/add_new_model.mdx

@@ -813,13 +813,9 @@ checkpoint and to get the required access rights to be able to upload the model
 *brand_new_bert*. The `push_to_hub` method, present in all models in `transformers`, is a quick and efficient way to push your checkpoint to the hub. A little snippet is pasted below:
 
 ```python
-brand_new_bert.push_to_hub(
-    repo_path_or_name="brand_new_bert",
-    # Uncomment the following line to push to an organization
-    # organization="<ORGANIZATION>",
-    commit_message="Add model",
-    use_temp_dir=True,
-)
+brand_new_bert.push_to_hub("brand_new_bert")
+# Uncomment the following line to push to an organization.
+# brand_new_bert.push_to_hub("<organization>/brand_new_bert")
 ```
 
 It is worth spending some time to create fitting model cards for each checkpoint. The model cards should highlight the

docs/source/en/model_sharing.mdx

@@ -179,10 +179,10 @@ This creates a repository under your username with the model name `my-awesome-mo
 >>> model = AutoModel.from_pretrained("your_username/my-awesome-model")
 ```
 
-If you belong to an organization and want to push your model under the organization name instead, add the `organization` parameter:
+If you belong to an organization and want to push your model under the organization name instead, just add it to the `repo_id`:
 
 ```py
->>> pt_model.push_to_hub("my-awesome-model", organization="my-awesome-org")
+>>> pt_model.push_to_hub("my-awesome-org/my-awesome-model")
 ```
 
 The `push_to_hub` function can also be used to add other files to a model repository. For example, add a tokenizer to a model repository: