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/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: