Add third-party tests for BeanieODM

[mdaffad]

Change Summary

Integrate beanie tests on third party test workflow, part of third party tests on #11160.
Workflow result - https://github.com/mdaffad/pydantic/actions/runs/12477146497

Related issue number

#11160

Checklist

• The pull request title is a good summary of the changes - it will be used in the changelog
• Unit tests for the changes exist
• Tests pass on CI
• Documentation reflects the changes where applicable
• My PR is ready to review, please add a comment including the phrase "please review" to assign reviewers

[codspeed-hq]

CodSpeed Performance Report

Merging #11177 will not alter performance

_{Comparing mdaffad:ci/third-party-beanie (7749fbf) with main (daa0732)}

Summary

✅ 46 untouched benchmarks

[github-actions]

Coverage report

This PR does not seem to contain any modification to coverable code.

[Viicos]

Thanks for the PR. This looks great

[sydney-runkle]

LGTM, let's wait for @Viicos' approval before we merge :)

[Viicos]

Thanks!