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[python-package] Add support for NumPy 2.0, test against nightly versions of dependencies (fixes #6454) (#6467)

* [python-package] Allow to pass early stopping min delta in params

* Fix test

* Add separate test

* Fix

* Add to cpp config

* Adjust test

* Adjust test

* Debug

* Revert

* Apply suggestions from code review

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Co-authored-by: James Lamb <jaylamb20@gmail.com>

[python-package] allow use of early_stopping_round<=0 to turn off early stopping (fixes #6401) (#6406)

* [python-package] fix mypy errors about callbacks

* revert unnecessary import

* [python-package] add type hints on Booster.update()

* add __boost()

* [python-package] add more type hints in engine.py

* Update python-package/lightgbm/engine.py
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* [python-package] add type hints on cv()

* remove inadvertent changes

* Apply suggestions from code review
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

[python-package] remove 'fobj' in favor of passing custom objective function in params (fixes #3244) (#5052)

* feat: support custom metrics in params

* feat: support objective in params

* test: custom objective and metric

* fix: imports are incorrectly sorted

* feat: convert eval metrics str and set to list

* feat: convert single callable eval_metric to list

* test: single callable objective in params
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* feat: callable fobj in basic cv function
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* test: cv support objective callable
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* fix: assert in cv_res
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* docs: objective callable in params
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* recover test_boost_from_average_with_single_leaf_trees
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* linters fail
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* remove metrics helper functions
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* feat: choose objective through _choose_param_values
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* test: test objective through _choose_param_values
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* test: test objective is callabe in train
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* test: parametrize choose_param_value with objective aliases
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* test: cv booster metric is none
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* fix: if string and callable choose callable
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* test train uses custom objective metrics
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* test: cv uses custom objective metrics
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* refactor: remove fobj parameter in train and cv
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* refactor: objective through params in sklearn API
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* custom objective function in advanced_example
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* fix whitespackes lint

* objective is none not a particular case for predict method
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* replace scipy.expit with custom implementation
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* test: set num_boost_round value to 20
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* fix: custom objective default_value is none
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* refactor: remove self._fobj
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* custom_objective default value is None
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* refactor: variables name reference dummy_obj
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* linter errors

* fix: process objective parameter when calling predict
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* linter errors

* fix: objective is None during predict call
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

[python-package] [R-package] propagate the best iteration of cvbooster into the individual boosters (#5066)

[python] fixes for supporting 2d numpy arrays for predictions, grads and hess in multiclass custom objective and eval (#5030)

* fixes for supporting 2d numpy arrays for predictions, grads and hess in multiclass custom objective

* Apply suggestions from code review
Co-authored-by: José Morales <jmoralz92@gmail.com>
Co-authored-by: José Morales <jmoralz92@gmail.com>

* clarify that categoricals will be converted to ints and not that they should be ints in the input data

* update remaining sections

* update config.h

* add suggestions

* make record_evaluation compatible with cv

* test multiple metrics in cv

* lint

* fix cv with train metric. save stdv as well

* always add dataset prefix to cv_agg

* remove unused function