Add initial logging framework to the extractor

[absurdlylongusername]

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

Setup initial logging API in the extractor that can be used globally throughout the extractor.

It should have an interface to set where logs are written to, so NewPipe can hook into it and send logs to Logcat

Why do you want this feature?

Refer to parent issue

Additional information

No response