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* [python-package] Test serialization and deserialization from in-memory string

Test case for #6851

* [python-package] Fill in `params` when loading from in-memory string

This fixes #6851 by using the same workaround as when loading the model
from a file.

* test_basic: use rng instead of legacy numpy RandomState

* test_basic: remove debug prints leftovers
Co-authored-by: James Lamb <jaylamb20@gmail.com>

* test_basic: add boolean, array of float and array of integers to testcase
Co-authored-by: James Lamb <jaylamb20@gmail.com>

* test_basic: make a cheaper model (2 rounds with 7 leaves each)
Co-authored-by: James Lamb <jaylamb20@gmail.com>

* test_basic: bugfix typos

* python_package_test: move string load test from basic to engine

* test_engine: catch params ignored warnings

* test_engine: be explicit about parameters assertion

* test_engine: shush linter complaint

* test_basic: delete empty line
Co-authored-by: James Lamb <jaylamb20@gmail.com>

* test_engine: even cheaper model with less features
Co-authored-by: James Lamb <jaylamb20@gmail.com>

* test_engine: delete redundant assert
Co-authored-by: James Lamb <jaylamb20@gmail.com>

* test_engine: run pre-commit and take it's word for it

* test_engine: be explicit in an E712 compliant way

* test_engine.py: pass different value as argument to make sure it is ignored

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Co-authored-by: James Lamb <jaylamb20@gmail.com>
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>