Log Level Filtering for PHP Built-in Server

Description

Hi,
We use the PHP 8.3 built-in server during development, and it has been very helpful. However, there is an excessive amount of stdout output. For every request to resources like images, JS, or CSS files, it logs messages such as Accepted, GET, Closing, etc.

Because of this, it becomes very difficult to see the stdout output or error messages from within the application itself. I couldn't find an option to filter these logs. A feature like loglevel could be helpful to manage this.

For example:
php -S 0.0.0.0:8086 -t ./public --loglevel 4

This would allow filtering logs based on levels (e.g., errors, warnings, info, etc.), making it easier to focus on application-specific outputs during development.

Additionally, the PHP built-in server outputs all logs to stderr, which seems like a bug. Ideally, standard logs should go to stdout and error messages to stderr.

PHP built-in server output like:

Start with the PHP 8.3 built-in server command path invoked by php -S, and trace how request logs and application errors are emitted. Define the expected log-level filtering and stdout/stderr behavior, then add coverage showing that selected messages are filtered and standard logs are separated from errors.