fix(ai): support Anthropic eager tool streaming compat

closes #3575

packages/coding-agent/docs/models.md

@@ -11,6 +11,7 @@ Add custom providers and models (Ollama, vLLM, LM Studio, proxies) via `~/.pi/ag
 - [Model Configuration](#model-configuration)
 - [Overriding Built-in Providers](#overriding-built-in-providers)
 - [Per-model Overrides](#per-model-overrides)
+- [Anthropic Messages Compatibility](#anthropic-messages-compatibility)
 - [OpenAI Compatibility](#openai-compatibility)
 
 ## Minimal Example
@@ -195,7 +196,7 @@ If your command is slow, expensive, rate-limited, or should keep using a previou
 | `contextWindow` | No | `128000` | Context window size in tokens |
 | `maxTokens` | No | `16384` | Maximum output tokens |
 | `cost` | No | all zeros | `{"input": 0, "output": 0, "cacheRead": 0, "cacheWrite": 0}` (per million tokens) |
-| `compat` | No | provider `compat` | OpenAI compatibility overrides. Merged with provider-level `compat` when both are set. |
+| `compat` | No | provider `compat` | Provider compatibility overrides. Merged with provider-level `compat` when both are set. |
 
 Current behavior:
 - `/model` and `--list-models` list entries by model `id`.
@@ -269,6 +270,38 @@ Behavior notes:
 - You can combine provider-level `baseUrl`/`headers` with `modelOverrides`.
 - If `models` is also defined for a provider, custom models are merged after built-in overrides. A custom model with the same `id` replaces the overridden built-in model entry.
 
+## Anthropic Messages Compatibility
+
+For providers or proxies using `api: "anthropic-messages"`, use `compat.supportsEagerToolInputStreaming` to control Anthropic fine-grained tool streaming compatibility.
+
+By default pi sends per-tool `eager_input_streaming: true`. If a proxy or Anthropic-compatible backend rejects that field, set `supportsEagerToolInputStreaming` to `false`. Pi will omit `tools[].eager_input_streaming` and send the legacy `fine-grained-tool-streaming-2025-05-14` beta header for tool-enabled requests instead.
+
+```json
+{
+  "providers": {
+    "anthropic-proxy": {
+      "baseUrl": "https://proxy.example.com",
+      "api": "anthropic-messages",
+      "apiKey": "ANTHROPIC_PROXY_KEY",
+      "compat": {
+        "supportsEagerToolInputStreaming": false
+      },
+      "models": [
+        {
+          "id": "claude-opus-4-7",
+          "reasoning": true,
+          "input": ["text", "image"]
+        }
+      ]
+    }
+  }
+}
+```
+
+| Field | Description |
+|-------|-------------|
+| `supportsEagerToolInputStreaming` | Whether the provider accepts per-tool `eager_input_streaming`. Default: `true`. Set to `false` to omit that field and use the legacy fine-grained tool streaming beta header on tool-enabled requests. |
+
 ## OpenAI Compatibility
 
 For providers with partial OpenAI compatibility, use the `compat` field.