Define best_iteration only if early stopping is used. (#9403)

* Define `best_iteration` only if early stopping is used.

This is the behavior specified by the document but not honored in the actual code.

- Don't set the attributes if there's no early stopping.
- Clean up the code for callbacks, and replace assertions with proper exceptions.
- Assign the attributes when early stopping `save_best` is used.
- Turn the attributes into Python properties.

---------

Co-authored-by: Philip Hyunsu Cho <chohyu01@cs.washington.edu>

doc/python/model.rst

@@ -37,3 +37,7 @@ The sliced model is a copy of selected trees, that means the model itself is imm
 during slicing.  This feature is the basis of `save_best` option in early stopping
 callback. See :ref:`sphx_glr_python_examples_individual_trees.py` for a worked example on
 how to combine prediction with sliced trees.
+
+.. note::
+
+   The returned model slice doesn't contain attributes like :py:class:`~xgboost.Booster.best_iteration` and :py:class:`~xgboost.Booster.best_score`.