- Add `is-compat` support to OpenAI compatibility model config, capabilities, hashing, and example config.
- Propagate `IsCompat` through API-key model resolution and switch OpenAI-compat executor translation to compatibility-aware routing.
- Keep Claude assistant thinking content in compatibility mode while keeping default behavior unchanged when `is-compat` is disabled.
Closes: #4776
- Added `is-compat` model metadata plumbing from config through executor and helpers, including hash computation.
- Introduced a compatibility-aware translation path (`TranslateRequestWithAPIKeyModelCompatibility`) and wired it into Claude/Gemini/Codex/Interactions request flows.
- Updated Claude message sanitization/translation behavior to keep empty-thinking compatibility blocks (including signatures) when `is-compat` is enabled, while keeping default behavior unchanged.
- Replaced instances of `thinking.ApplyThinking` with `helps.ApplyRequestThinking` across all executors for consistency.
- Updated `applyGeminiInteractionsThinking` to accept `cliproxyexecutor.Request` and `Options`.
- Centralized logic for request thinking application to `helps` package for improved maintainability.
Closes: #4618
