I propose a __sk_clone__ method that clone calls (if the method exist). This way arbitrary objects can define how they want to be cloned. This is similar to mechanism behind __sk_is_fitted__ + check_is_fitted.

Purpose

There are PR that run into issues with clone, and it would be nice to allow the estimator to define how it wants to be cloned.

1. Metadata routing: Base sample-prop implementation and docs #21284 Needed to change clone to copy an private attribute that is configured outside of __init__
2. Search spaces in estimator: Initial implementation of GridFactory #21784 (comment) the search space itself needs to be copied over when clone gets called.
3. Ability to customize cloning: Strict identity parameter check in sklearn.base.clone #15371 (comment)