Bump beartype from 0.20.2 to 0.22.2

Bumps [beartype](https://github.com/beartype/beartype) from 0.20.2 to 0.22.2.
- [Release notes](https://github.com/beartype/beartype/releases)
- [Changelog](https://github.com/beartype/beartype/blob/main/doc/RELEASE.rst)
- [Commits](beartype/beartype@v0.20.2...v0.22.2)

---
updated-dependencies:
- dependency-name: beartype
  dependency-version: 0.22.2
  dependency-type: direct:production
  update-type: version-update:semver-minor
...

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

Author: dependabot[bot]

pyproject.toml

@@ -30,7 +30,7 @@ dependencies = [
     "deepdiff==8.6.1",
     "numpy>=1.22.2,<2.3.0",
     "matplotlib==3.10.3",
-    "beartype==0.20.2",
+    "beartype==0.22.2",
     "jaxtyping==0.3.2",
     "deprecated>=1.2.14"
 ]