Round 5 review flagged two asymmetries:
1. Kimi web-search bypass hard-capped stops at 4 while the default OAI-compat path honours provider_info["stop_max"]. Apply the same provider-aware logic in _stream_kimi_web_search so kimi-with-search and kimi-without-search match. Also add Kimi's documented 5-stop max (https://platform.kimi.ai/docs/api/chat) to the provider registry so the cap actually fires.
2. chat-settings-sheet.tsx caps every non-Anthropic external provider at 4 stops. Replace with a per-provider getProviderStopMax helper in provider-capabilities.ts so DeepSeek, Mistral, and local backends are not artificially restricted while OpenAI Chat still hits its 4-entry hard limit and Kimi hits its documented 5-entry cap.
Tests pin the Kimi 5-cap on both Kimi paths.