Replace mypy with pyright

[emdneto]

We currently use Pyright in the contrib repository. However, in the core repository, Pyright is configured with typeCheckingMode = "off". During the SIG meeting on 01/09/2025, we discussed and agreed to replace mypy with Pyright in the core repository as well. This change will ensure both repositories use the same type checker, improving consistency across the codebase.

[pierceroberts]

Hello @emdneto !
I am looking to contribute to the project if I can and this seemed doable!
I looked into this a bit and would like you the mypy.ini, mypy-requirements.txt, and mypy-relaxed.ini deleted in addition to the lines in toml referring to mypy?

In addition I noticed this pyright isn't set up in the pre-commit yaml in either repos you mentioned above. Do you want the pre-commit hooks updated too?
Cheers!

[Kludex]

It should be analogous to this: open-telemetry/opentelemetry-python-contrib#3116

[xrmx]

I think we can close this