refactor(conversations): consume the shared OpenAI operation match

[leseb]

Description

Make the OpenAI Conversations handler consume the typed operation match produced by openai_operation instead of independently identifying the same method/path pair.

Parent epic: #740

Scope

• Use the shared operation match as the authoritative Conversations operation identity.
• Preserve access to required path parameters for local handlers.
• Use registry request-body metadata to decide whether body processing is required.
• Preserve fail-closed local handling and existing storage behavior.
• Keep runtime routes, Rust contract types, generated implementation OpenAPI, and pinned conformance checks linked.
• Remove redundant Conversations route-identification logic once the shared match owns it.

Acceptance Criteria

• All supported Conversations operations retain their current local behavior.
• Unsupported methods and malformed paths do not enter Conversations handlers.
• Bodyless operations do not trigger body parsing.
• Required path parameters are available without cloning the request URI.
• Existing positive, negative, persistence, and conformance tests remain green.
• Focused functional coverage proves openai_operation and openai_conversations compose correctly.

Dependencies

• refactor(openai): generalize the operation registry and matcher #746 — shared operation registry and matcher
• feat(openai): add a request-head operation classifier #744 — openai_operation classifier

Related Work

• Epic: Resolve OpenAI Conversations contract conformance drift #565 — Conversations contract conformance drift

Area

Provider APIs (OpenAI/Anthropic)

[eoinfennessy]

Hey @cdoern, is it okay if I assign myself to this? I started planning this with Codex and quickly realised it depends on #890. I don't want to get in the way if you are already planning to work on this after that PR lands.