fix(ai): support OpenRouter session affinity (#6496)

Fixes #6366

packages/coding-agent/docs/custom-provider.md

@@ -722,6 +722,8 @@ interface ProviderModelConfig {
     thinkingFormat?: "openai" | "openrouter" | "deepseek" | "together" | "zai" | "qwen" | "chat-template" | "qwen-chat-template" | "string-thinking" | "ant-ling";
     chatTemplateKwargs?: Record<string, string | number | boolean | null | { "$var": "thinking.enabled" | "thinking.effort"; omitWhenOff?: boolean }>;
     cacheControlFormat?: "anthropic";
+    sessionAffinityFormat?: "openai" | "openai-nosession" | "openrouter";
+    sendSessionAffinityHeaders?: boolean;
 
     // anthropic-messages
     supportsEagerToolInputStreaming?: boolean;

packages/coding-agent/docs/models.md

@@ -445,6 +445,8 @@ For providers with partial OpenAI compatibility, use the `compat` field.
 | `thinkingFormat` | Use `reasoning_effort`, `openrouter`, `deepseek`, `together`, `zai`, `qwen`, `chat-template`, or `qwen-chat-template` thinking parameters |
 | `chatTemplateKwargs` | `chat_template_kwargs` values for `thinkingFormat: "chat-template"`; use `{ "$var": "thinking.enabled" }` or `{ "$var": "thinking.effort" }` for pi-controlled thinking values |
 | `cacheControlFormat` | Use Anthropic-style `cache_control` markers on the system prompt, last tool definition, and last user/assistant text content. Currently only `anthropic` is supported. |
+| `sendSessionAffinityHeaders` | For `openai-completions`, send session-affinity headers from the session id when caching is enabled. Default: `false`. |
+| `sessionAffinityFormat` | For `openai-completions` and `openai-responses`, the session-affinity header format: `openai` sends `session_id`/`x-client-request-id` (completions also `x-session-affinity`), `openai-nosession` omits the underscore-containing `session_id` header, `openrouter` sends `x-session-id`. Does not affect the `prompt_cache_key` body param. Default: auto-detected. |
 | `supportsStrictMode` | Include the `strict` field in tool definitions |
 | `supportsLongCacheRetention` | Whether the provider accepts long cache retention when cache retention is `long`: `prompt_cache_retention: "24h"` for OpenAI prompt caching, or `cache_control.ttl: "1h"` when `cacheControlFormat` is `anthropic`. Default: `true`. |
 | `openRouterRouting` | OpenRouter provider routing preferences. This object is sent as-is in the `provider` field of the [OpenRouter API request](https://openrouter.ai/docs/guides/routing/provider-selection). |