feat: support customizing system-prompt in exec

[breezewish]

Close #6023

For now system prompt can be switched via /prompt in interactive mode. But in non-interactive mode there is no way to do this. All conversations are sent with the default system prompt "You are Codex, based on GPT-5...". This PR adds support for customizing the system-prompt for the non-interactive mode (exec).

The --system-prompt parameter usage is similar to Claude Code, just accepts prompts inline.

With this feature, people could have exactly the same effect as /review using the review system prompt in exec, or whatever system prompt he/she likes.

I manually verified it works by reviewing the LLM stream:

cargo run --bin codex --release -- exec --skip-git-repo-check --system-prompt "you are a helpful agent" -

[github-actions]

All contributors have signed the CLA ✍️ ✅
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[breezewish]

I have read the CLA Document and I hereby sign the CLA

[etraut-openai]

Thanks for the contribution. Which bug report is this related to? The link points back to this PR rather than an issue.

[breezewish]

@etraut-openai Oh sorry, wrong link. Fixed. It should be #6023

[etraut-openai]

@codex review

[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. Hooray!

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[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. You're on a roll.

ℹ️ About Codex in GitHub

Your team has set up Codex to review pull requests in this repo. Reviews are triggered when you

• Open a pull request for review
• Mark a draft as ready
• Comment "@codex review".

If Codex has suggestions, it will comment; otherwise it will react with 👍.

Codex can also answer questions or update the PR. Try commenting "@codex address that feedback".

[etraut-openai]

Thanks for the contribution. We've updated our contribution guidelines to clarify that we're currently accepting contributions for bugs and security fixes, but we're not generally accepting new features at this time. We need to make sure that all new features compose well with both existing and upcoming features and fit into our roadmap.

This is a feature we'd like to add, but we need to give more thought to how to expose it. We don't have the bandwidth to do the necessary design work at this time, but we will get to it eventually. We are using upvotes (thumbs-up reactions) to help inform guide our prioritization of features.