## Summary
- Expand the hosted web search prompt with explicit Markdown-link
citation guidance.
- Keep internal `turnX` reference IDs out of final responses and place
citations next to supported claims.
## Context
https://openai.slack.com/archives/C0AU83S0ZQU/p1781133381448499?thread_ts=1780352049.512299&cid=C0AU83S0ZQU
## Test plan
- Confirmed `codex-rs/ext/web-search/web_run_description.md` exactly
matches the supplied target prompt.
- `UV_CACHE_DIR=/tmp/codex-uv-cache
PATH=/tmp/codex-just/bin:/home/dev-user/.rustup/toolchains/1.95.0-x86_64-unknown-linux-gnu/bin:$PATH
python3 scripts/format.py --check`
- `git diff --check`
## Summary
- Update the web search tool prompt to require Markdown links for cited
sources.
- Explicitly tell the model not to use `turnX`-style citations in
responses.
## Context
https://openai.slack.com/archives/C0AU83S0ZQU/p1780964147777649?thread_ts=1780352049.512299&cid=C0AU83S0ZQU
## Test plan
- `git diff --check`
- `python3 scripts/format.py --check` (fails only on Rust formatter
setup: rustup cannot create temp files under `/home/dev-user/.rustup`;
Just and Python formatter checks pass when using temp cache dirs)
yuning-oai