Warning consistency and configuration?

Probably mostly related to arviz-stats but also related to inferencedata schema checks and rcParams. There are several places throughout the library where we emit warnings (I think sometimes through warnings.warn others logger.warning) that are about issues with the model, approximations potentially failing...

I was thinking if we might want to ensure some consistency among them and/or add a "verbosity" rcParam to allow turning them off.

Re consistency, having a "ModelingWarning" or "BayesianWorkflowWarning" might be interesting but these types of warnings might be better suited as logging messages? I always struggle with the difference between the two.

Re configuration, if we were to add a custom warning class we can ignore as it is easy for users to turn them off. Otherwise, I imagine running models on a cloud service or HPC and including loo there for example. I'd check the warnings of the elpddata output later on locally, but would rather keep the computation logs for other things.

Start by inventorying the warning sites mentioned across arviz-stats, inference-data schema checks, and rcParams, including uses of warnings.warn and logger.warning. Decide whether consistency or configurable verbosity is the goal, then define how users would control the resulting warnings or logs and verify the behavior across those areas.