Add build-types to release workflows (#50396)

Summary:
Pull Request resolved: https://github.com/facebook/react-native/pull/50396

Integrates the `yarn build-types` script into our CI workflows.

**Notes**

- Will validate type generation in future PRs as part of the `test-all` workflow (this has been stable (i.e. successfully runs for our codebase) for the last 3 weeks).
- This is not load bearing in production code until D71969602.

Changelog: [Internal]

Reviewed By: cortinico

Differential Revision: D71975705

fbshipit-source-id: a234a05008b5e75976bbd5258948c37fcc1eeb76