I think OpenAI has actually released an official version of exactly this: https://community.openai.com/t/introducing-codex-plugin-for-...

https://github.com/openai/codex-plugin-cc

I actually work the other way around. I have codex write "packets" to give to claude to write. I have Claude write the code. Then have Codex review it and find all the problems (there's usually lots of them).

Only because this month I have the $100 Claude Code and the $20 Codex. I did not renew Anthropic though.