I recently started using pywikibot. I have never used a python library before with this kind of custom verbose by default logging.
I suggest you remove all custom logging code and just support the normal logging levels like requests, WikibaseIntegrator and most other python libraries.
Let the user setup logging themselves as needed.
Could you please explain a bit more. What is wrong with the current implementation, what is the advantage to remove it? How to replace the custom levels with defaults?
Please reopen and make more specific suggestions e.g.
Feature summary (what you would like to be disable to do and where):
Use case(s) (list the steps that you performed to discover that problem, and describe the actual underlying problem which you want to solve. Do not describe only a solution):
Benefits (why should this be changed?):