Fix `uvicorn` logging when in Vertex AI

## Description

At the moment, when using the latest wheel via the Hugging Face DCL in Google `us-docker.pkg.dev/deeplearning-platform-release/gcr.io/huggingface-pytorch-inference-cu121.2-2.transformers.4-41.ubuntu2204.py311`, the logs are not dumped within Google Cloud Logging, and that's due to the default `uvicorn` logging configuration.

> [!NOTE]
> **EDIT**: Those are indeed dumped, just that some logs take a while to appear within Google Cloud. But the logging messages on a per-request basis are missing, meaning that only failures are notified, so we could still try to add some logging messages for each incoming request.

Additionally, besides the default `uvicorn` logs on start up, GET/POST requests, etc. we should also add more `logging` messages within the inference interface to see what's going on when the inference is running to better debug the errors if any.