The new GPT-5-Codex model isn't yet available in the API, so if you want to try that model using the Codex CLI tool the only way to do that is with a ChatGPT account (I'm more sure if the free account has it, the $20/month definitely does). You need to then authenticate Codex CLI with ChatGPT.

OpenAI say API access to that model is coming soon, at which point till be able to use it in Codex CLI with an API key and pay for tokens as you go.

You can also use the Codex CLI tool without using the new GPT-5-Codex model.

You can use Codex CLI with an API key instead of a subscription, but then you won't have access to this new GPT-5 Codex model, since it's not out on the API yet. But normal GPT-5 in Codex is perfectly fine.