Make it easy to get seperate "prints" for individual runs/ users when using Transformers Agent
### Feature request

I have started exploring the new Transformers Agent. And I would like to build a UI to help me speed up the process.

I might be running multiple runs in parallel or have multiple users using my application. I would like to be able to stream the information from the run as it arrives. I would like to store the information in a database containing all the runs I've done.

Currently all the valuable information about the run is printed I.e. you are using print to inform me like below

```bash
==Explanation from the agent==
I will use the following  tool: `image_generator` to generate an image.


==Code generated by the agent==
image = image_generator(prompt="rivers and lakes")


==Result==
<PIL.PngImagePlugin.PngImageFile image mode=RGB size=512x512 at 0x7F8DDC11C4C0>
```

This is for example done in `agenst.py`

![image](https://github.com/huggingface/transformers/assets/42288570/ed635571-63f2-45b4-9cc5-8acd33dcbc71)

Using `print` makes it hard for me to distinguish between multiple runs/ users. Especially if run in parallel.

Please provide a simple to use method to stream each run individually. It could be as simple as adding a `print` (or `write`) argument to the `Agent.run`, `HFAgent.run` and `OpenAI.run` method.

Alternatively some `run_id` argument could be provided and printed as well. Then I can split the stream that comes in by `run_id`. This is less preferred though that this also adds some complexity.

### Motivation

This will make it much, much easier to create interesting AI apps.

### Your contribution

I might do it 😄 . But I hope someone with knowledge of the code base would do it.

### Additional Context

An async `.run_async` function would also be much appreciated as my UI is built on top of Tornado. This will help me keep the app responsive.
The solution for me is probably to inspect the `run` function and then compose the pieces in a way that works better for my app.

![image](https://github.com/huggingface/transformers/assets/42288570/956130ff-ff3c-42e1-8762-840c2df73aad)<|||||>cc @sgugger @LysandreJik <|||||>Would the PR mentioned above fix your problem?