I think there’s some misunderstanding. Codex’s official CLI lets users choose between low/med/high reasoning and I believe these tune the adaptive reasoning, so high will generally prefer more reasoning but it may still finish quickly in trivial cases. I was also surprised Cursor does not provide low/medium/high variants for Codex.
GPT-5-Codex is only available in the Responses API and supports low, medium, and high
reasoning_efforts
https://platform.openai.com/docs/guides/latest-model#faq
https://www.perplexity.ai/search/gpt-5-codex-in-api-does-it-sup-xEOhgpfxQ.GIhc6l9wFItw#0
PS. Possible duplicate thread: Why is there no gpt-5-codex-(high|medium|low)