docs: update main repo documentations files to reference basedpyright instead of pyright

Author: 56kyle

README.md

@@ -85,7 +85,7 @@ This is a really brief/condensed idea of what is planned for this template, and
 <details>
 <summary>Click to expand</summary>
 
-- [x] Swap to UV, Ruff, and Pyright (maybe ty later, but at the moment of writing this isn't ready yet)
+- [x] Swap to UV, Ruff, and Basedpyright (maybe ty later, but at the moment of writing this wasn't ready yet)
 - [x] Add cruft and commitizen
 - [x] Centralize CI/CD through noxfile using uv cache to maintain speed
 - [x] Add CI/CD for GitHub, Gitlab, and Bitbucket (Only GitHub guaranteed to work, but others should be close enough)

{{cookiecutter.project_name}}/CONTRIBUTING.md

@@ -121,7 +121,7 @@ This project follows these standards:
 
 - **Code formatting:** [Ruff][ruff-documentation] (automatically applied by pre-commit)
 - **Linting:** Ruff with comprehensive rule set
-- **Type checking:** [Pyright][pyright-documentation]
+- **Type checking:** [Basedpyright][basedpyright-documentation]
 - **Security:** [Bandit][bandit-documentation] for security linting
 - **Commit messages:** [Conventional Commits][conventional-commits] format preferred
 - **Testing:** [pytest][pytest-documentation] with good coverage
@@ -168,7 +168,7 @@ Common Nox sessions for development:
 # Code quality
 uvx nox -s format-python    # Format with Ruff
 uvx nox -s lint-python      # Lint with Ruff
-uvx nox -s typecheck        # Type check with Pyright
+uvx nox -s typecheck        # Type check with Basedpyright
 uvx nox -s security-python  # Security checks
 
 # Testing
@@ -206,6 +206,7 @@ _This project was generated from the [cookiecutter-robust-python][cookiecutter-r
 {% if cookiecutter.repository_provider == 'github' %}[discussions]: https://{{ cookiecutter.repository_host }}/{{ cookiecutter.repository_path }}/discussions{% endif %}
 [uv-documentation]: https://docs.astral.sh/uv/
 [ruff-documentation]: https://docs.astral.sh/ruff/
+[basedpyright-documentation]: https://github.com/detachhead/basedpyright
 [pyright-documentation]: https://github.com/microsoft/pyright
 [bandit-documentation]: https://bandit.readthedocs.io/
 [conventional-commits]: https://www.conventionalcommits.org/