core: Cleanup Pydantic models and handle deprecation warnings (#30799)
* Simplified Pydantic handling since Pydantic v1 is not supported
anymore.
* Replace use of deprecated v1 methods by corresponding v2 methods.
* Remove use of other deprecated methods.
* Activate mypy errors on deprecated methods use.
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Co-authored-by: Eugene Yurtsev <eyurtsev@gmail.com>