perf(openapi): cache serialized openapi document

[ZhuchkaTriplesix]

Context

• GET /openapi.json is served from state.openapi mutex; both sync and async paths call openapi.lock().to_string() per request (src/dispatch.rs).
• OpenAPI document changes only at route registration / title update.

Problem

Repeated serialization and lock contention on a read-mostly document.

Proposed change

• Cache serialized document as Arc<str> or Bytes on AppState.
• Invalidate cache when routes are added, title changes, or OpenAPI is toggled.
• Aligns with partial completion of backlog perf: reduce lock contention on route match (RWLock or route snapshot) #4 (route snapshot done; openapi lock remains).

Files

• src/state.rs, src/lib.rs, src/dispatch.rs

Acceptance criteria

• /openapi.json body identical before/after change.
• No per-request full JSON serialization on cache hit.
• Tests cover route add and title change invalidation.

Expected low-level impact

Faster OpenAPI endpoint; less mutex work under load.