Cleanup OpenAI docs publishing

[danieljurek]

Custom logic was added to enable basic publishing of the OpenAI readme documentation on the docs site (ref docs were not supported at the time of the change). This work should be reverted once the docs team supports the package.

Reversion should only require reverting changes in this PR: #31788

[github-actions]

Thanks for the feedback! We are routing this to the appropriate team for follow-up. cc @glharper.