feat(openai): support finite chat continuations

[franciscojavierarceo]

Summary

• Support finite previous_response_id continuations when a Responses API client targets a backend that only implements /v1/chat/completions.
• Fail closed if stored history was not rehydrated, preventing silent loss of prior turns.
• Add the required store/rehydrate example pipeline, two-turn functional coverage, and a controlled synthetic inference replay that binds the prior generated response ID.

Related issue

Finite request/response translation follows up on #35. Streaming response conversion remains tracked in #36.

Validation

• Unit tests: make test
• Integration or functional tests: make test and make test-inference-fixtures
• make lint
• Rustdoc: make doc

Checklist

• I reviewed every changed line and can explain the change.
• New capabilities include an example config and functional example test.
• User-facing behavior and generated documentation are updated.
• Performance-sensitive changes include appropriate benchmark or load-test evidence. Not applicable: no new buffering, cloning, or hot-path work was added.
• Commits are signed and include a Signed-off-by trailer.

Pre-landing review

Claude and Codex reviews found no remaining actionable issues after strengthening the inference fixture to cover a real two-turn stored continuation.

Breaking changes

None. Requests without previous_response_id are unchanged. Streaming continuation response translation remains outside this change and is tracked in #36.

[Copilot]

Pull request overview

Adds finite stored continuation support when translating OpenAI Responses requests to Chat Completions backends.

Changes:

• Rehydrates prior response history and fails closed when finite history is unavailable.
• Adds response storage to the example pipeline and two-turn integration coverage.
• Extends inference fixtures with dynamic response-ID binding and synthetic replay coverage.

Reviewed changes

Copilot reviewed 14 out of 14 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
tests/utils/src/inference_fixture/schema.rs	Adds previous-response ID binding.
tests/utils/src/inference_fixture/replay.rs	Binds IDs during fixture replay.
tests/utils/src/inference_fixture/record.rs	Binds IDs during live recording.
tests/utils/src/inference_fixture/coverage.rs	Validates new fixture coverage.
tests/integration/tests/suite/examples/responses_to_chat_completions.rs	Tests stored continuations and missing history.
tests/integration/fixtures/inference/scenarios/responses/chat-basic-nonstream.yaml	Defines a two-turn continuation scenario.
tests/integration/fixtures/inference/recordings/synthetic/responses/chat-basic-nonstream.json	Records synthetic continuation behavior.
tests/integration/fixtures/inference/README.md	Documents fixture binding and coverage.
tests/integration/fixtures/inference/coverage.yaml	Registers translation coverage.
examples/README.md	Updates the example description.
examples/configs/openai/responses/responses-to-chat-completions.yaml	Adds storage and rehydration filters.
docs/filters/responses_to_chat_completions.md	Documents continuation requirements.
apis/src/openai/responses/responses_to_chat_completions/tests.rs	Adds translation and fail-closed tests.
apis/src/openai/responses/responses_to_chat_completions/mod.rs	Enforces finite-history rehydration.

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