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)

[OlegGirko]

This becomes urgent.

Fedora 43 (to be released in less than month) switches to Python 3.14 and to Pydantic 2.12.0 that supports Python 3.14.
However, compatibility code in pydantic.v1 does not support Python 3.14, and now tests fail as a result.

One of issues is this: pydantic/pydantic#12363, but there are other issues.

The first comment of this issue says:

pydantic.v1 is a verbatim copy of the latest Pydantic V1, so both are not meant to be supported in 3.14.

So, Pydantic developers are not going to fix this.

Please switch to normal Pydantic V2 instead of unsupported and outdated pydantic.v1 ASAP. This is urgent. Otherwise, there is no way to make Synapse work in Fedora 43.