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@glemaitre and @adrinjalali I think this is ready for reviews. I implemented the changes discussed during some drafting meetings compared to #27663.

A quick summary.

From the point of view of a user:

• callback objects are available from sklearn.callback. In this PR, only ProgressBar is implemented.
• callbacks are registered to estimators using the set_callbacks(ProgressBar()).
• if I want to enable the ProgressBar to all inner steps of my pipeline: ProgressBar(max_estimator_depth=None). Limited to depth=1 by default for performance considerations.

From the point of view of a third party developer of estimators:

• Callback support is enabled through the CallbackSupportMixin
• A CallbackContext object must be created at the beginning of fit (using init_callback_context from the mixin). This object is then used to create sub-contexts for subtasks, evaluate the callback hooks, and eventually propagate the callbacks to sub-estimators.

From the point of view of a third party developer of callbacks:

• Callbacks must follow the CallbackProtocol protocol (3 hooks essentially).
• Callbacks that should be propagated to inner estimators must follow an additional protocol.
• The 3 hooks, receive different args. Their signature will be refined and better documented in follow-up PRs. One key arg is the node of the current task, which is a TaskNode object and is useful to find at which step the hook was called and take actions upon that.