Update pydantic to >= 2

[matrixbot]

This issue has been migrated from #15979.

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Adapt codebase to use pydantic >= 2 models and functionalities.

Remove unneeded checks from scripts-dev/check_pydantic_models.py, since pydantic can now be used in a strict mode which will prevent the type coercion:
https://docs.pydantic.dev/2.0/usage/strict_mode/#type-coercions-in-strict-mode

Closes #15858

Pull Request Checklist

• Pull request is based on the develop branch
• Pull request includes a changelog file. The entry should:
  • Be a short description of your change which makes sense to users. "Fixed a bug that prevented receiving messages from other servers." instead of "Moved X method from EventStore to EventWorkerStore.".
  • Use markdown where necessary, mostly for code blocks.
  • End with either a period (.) or an exclamation mark (!).
  • Start with a capital letter.
  • Feel free to credit yourself, by adding a sentence "Contributed by @github_username." or "Contributed by [Your Name]." to the end of the entry.
• Pull request includes a sign off
• Code style is correct
  (run the linters)