chore(deps): bump pydantic-settings in /reference-apps/fastapi-api-first

Bumps [pydantic-settings](https://github.com/pydantic/pydantic-settings) from 2.12.0 to 2.13.1.
- [Release notes](https://github.com/pydantic/pydantic-settings/releases)
- [Commits](pydantic/pydantic-settings@v2.12.0...v2.13.1)

---
updated-dependencies:
- dependency-name: pydantic-settings
  dependency-version: 2.13.1
  dependency-type: direct:production
  update-type: version-update:semver-minor
...

Signed-off-by: dependabot[bot] <support@github.com>

Author: dependabot[bot]

reference-apps/fastapi-api-first/requirements.txt

@@ -4,7 +4,7 @@
 # Core FastAPI dependencies
 fastapi==0.128.0
 uvicorn[standard]==0.40.0
-pydantic-settings==2.12.0
+pydantic-settings==2.13.1
 slowapi==0.1.9  # Rate limiting
 pybreaker==1.4.1  # Circuit breaker