[Feature] Add robust logging to the extractor

Checklist

• I am aware that this issue is being opened for the NewPipe Extractor, NOT the app, and my feature request will be dismissed otherwise.
• I made sure that there are no existing issues - open or closed - which I could contribute my information to.
• I have taken the time to fill in all the required details. I understand that the feature request will be dismissed otherwise.
• This issue contains only one feature request.
• I have read and understood the contribution guidelines.

Feature description

Add logs to the extractor. Currently, the extractor has no logging whatsoever, which makes it practically impossible to debug issues without having to manually step through code when debugging or using custom console log statements.

The end goal of this issue is so that the logs present a clear picture of actions done in the extractor so that anyone who reads it will have a clear timeline of what occurs, and be able to diagnose problems easier without having to manually debug to pinpoint where errors occur.

The complete ideal implementation of this should allow logging to be enabled/disabled based on config settings.

The logging should be divided into sections, with each section/level toggleable via the config settings.

E.g. Verbose, Information, Trace.

Can also have sections for certain components of the extractor depending on which logs you want printed. Like if you only care about SoundCloud logs, or Comments, or etc.

Why do you want this feature?

Helps for diagnostics and transparency, to make debugging and bug reporting easier for devs and users.

Additional information

No response

Start by reviewing the extractor's existing architecture and configuration needs, since no files, tests, or entry points are identified. Define the logging sections, levels, and enable/disable settings before implementation. Done should provide configurable logs that show a clear timeline of extractor actions and support diagnosing failures.