fix: web search call output ordering

[maralbahari]

Summary

Fixes #156 by preserving upstream output_index ordering for streaming web_search_call items relative to reasoning, messages, and other output items.

• Tracks web search calls from response.output_item.added through response.output_item.done, with fallback support for providers that omit the added event.
• Preserves all documented web-search action variants: search, open_page, and find_in_page.
• Omits unfinished synthetic placeholders rather than returning fabricated completed calls.
• Reconciles missing or late item IDs without duplicating output items.
• Adds accumulator regressions and recorder-generated gateway/OpenAI streaming and non-streaming cassettes.

Test Plan

• cargo test --workspace -- --test-threads=8
• cargo clippy --all-targets -- -D warnings
• cargo fmt --all -- --check
• GitHub checks: DCO, pre-commit, Rust, and container build/smoke test

[franciscojavierarceo]

I prepared and validated the follow-up for the accumulator issues found in review:

• preserve all documented web-search action variants (search, open_page, and find_in_page)
• omit unfinished synthetic web-search placeholders
• reconcile missing/late item IDs without duplicate output items

The fix is commit 3cabd2e on vllm-project:codex/pr-157-fix. This PR has maintainer edits disabled and the authenticated maintainer account has no push permission on EmbeddedLLM/agentic-api, so I cannot attach the commit to the head branch directly. Please either cherry-pick 3cabd2e onto bugfix-websearch-acc-order or enable maintainer edits.

Verification: cargo test --workspace, cargo clippy --all-targets --workspace -- -D warnings, cargo fmt --all -- --check, and git diff --check all pass.

[maralbahari]

I prepared and validated the follow-up for the accumulator issues found in review:

• preserve all documented web-search action variants (search, open_page, and find_in_page)
• omit unfinished synthetic web-search placeholders
• reconcile missing/late item IDs without duplicate output items

The fix is commit 3cabd2e on vllm-project:codex/pr-157-fix. This PR has maintainer edits disabled and the authenticated maintainer account has no push permission on EmbeddedLLM/agentic-api, so I cannot attach the commit to the head branch directly. Please either cherry-pick 3cabd2e onto bugfix-websearch-acc-order or enable maintainer edits.

Verification: cargo test --workspace, cargo clippy --all-targets --workspace -- -D warnings, cargo fmt --all -- --check, and git diff --check all pass.

thanks I also re-recoded the cassettes and added integration test for web search action.

[franciscojavierarceo]

The ordering fix, documented web-search action variants, provisional-item handling, and missing-ID reconciliation are covered by focused regressions and recorded gateway/OpenAI comparisons. The final head is mergeable and all required checks pass.