Fix(db): Ensure Cloud SQL Connector is fork-safe with Gunicorn

Created by: Edouard-Legoupil

The FastAPI application was crashing during login when deployed with Gunicorn and multiple workers. This was caused by the Google Cloud SQL Connector being initialized before Gunicorn forked its worker processes. The connector is not fork-safe, leading to unstable connections and crashes in the child processes.

This commit refactors the database initialization logic to be lazy. The Cloud SQL Connector is now initialized once per worker process upon its first database connection attempt. This is the recommended pattern for using non-fork-safe resources with pre-forking servers like Gunicorn.

Additionally, this commit improves the application's logging infrastructure:

• supervisord is configured to forward application logs to the container's stdout/stderr.
• The FastAPI application's logging is configured to stream to stdout instead of a file.
• print statements in the authentication API have been replaced with proper logging calls.

These changes ensure application stability and improve diagnostics in a containerized environment.

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