Bump pydantic from 2.9.2 to 2.11.1 (#1161)

Bumps [pydantic](https://github.com/pydantic/pydantic) from 2.9.2 to 2.11.1.
- [Release notes](https://github.com/pydantic/pydantic/releases)
- [Changelog](https://github.com/pydantic/pydantic/blob/main/HISTORY.md)
- [Commits](pydantic/pydantic@v2.9.2...v2.11.1)

---
updated-dependencies:
- dependency-name: pydantic
  dependency-type: direct:production
  update-type: version-update:semver-minor
...

Signed-off-by: dependabot[bot] <[email protected]>
Co-authored-by: dependabot[bot] <49699333+dependabot[bot]@users.noreply.github.com>

Author: dependabot[bot]

pyproject.toml

@@ -109,7 +109,7 @@ strict = [
     "numpy",
     "phonopy==2.30.1",
     "pydantic-settings==2.7.0",
-    "pydantic==2.11.1",
+    "pydantic==2.11.2",
     "pymatgen-analysis-defects==2025.1.18",
     "pymatgen==2025.2.18",
     "pymongo==4.10.1",