docs: update pydantic docs accordingly Pydantic V2

[plusiv]

Updated the Pydantic Serialization Tutorial documentation accordingly to the new API by replacing the .dict() and .json() by the new ones. Additionally changed __root__ attribute by root from the new RootModel.

Description

Methods .json() and .dict were deprecated in the new Pydantic V2 API, this changes aims to change the related pydantic documentation regarding Pydantic Serialization Tutorial to the new methods.

New methods replacements are:

• .dict() → .model_dump()
• .json() → .model_dump_json()

See migration guide.

Regarding the __root__ field, since they decoupled the "custom root model" with the new type RootModel, that usage was changed in documentation as well.

Motivation and Context

Pydantic Migration Guide

How Has This Been Tested?

N/A

Checklist:

• [x] My code follows the code style of this project.
• [x] My change requires a change to the documentation.
• [x] I have updated the documentation accordingly.
• [ ] I have added the changelog accordingly.
• [x] I have read the CONTRIBUTING document.
• [ ] I have added tests to cover my changes.
• [x] All new and existing tests passed.

[long2ice]

Thanks!