fix(claude): add Claude-compatible thinking replay persistence for multi-turn sessions

- Add Claude replay enablement and scope derivation for API-key compatible Claude requests with isolated model/session keys.
- Restore cached signed reasoning blocks into outbound requests and persist completed assistant turns after execution, including stream handling.
- Introduce a dedicated Claude thinking-replay cache with local + home-KV paths, CAS-based snapshot replace/clear, TTL/size limits, and bounded eviction/expiration management.

Closes: #4856