feat(coding-agent): accept native extension providers

Allow extensions to register complete pi-ai Provider objects while preserving models.json composition and resolved provider auth access.

Refs #4823 and #4824.

packages/coding-agent/docs/extensions.md

@@ -977,7 +977,7 @@ ctx.sessionManager.getLeafId()              // Current leaf entry ID
 
 ### ctx.modelRegistry / ctx.model
 
-Access to models and API keys.
+Access to models, providers, and resolved authentication. `ctx.modelRegistry.getProvider(id)` returns the effective pi-ai provider, while `getProviderAuth(id)` resolves its current API key, headers, base URL, and provider-scoped environment without requiring a loaded model. `ctx.model` is the active model.
 
 ### ctx.signal
 
@@ -1679,7 +1679,37 @@ Calls made during the extension factory function are queued and applied once the
 
 Dynamic providers can implement `refreshModels`. Pi calls it during model refresh, publishes the returned list synchronously through the provider, and passes the canonical credential/store/network/signal context. The extension decides whether to persist the catalog through `context.store`; live servers such as llama.cpp can ignore it.
 
+Extensions that need native provider auth, filtering, refresh, or stream behavior can register a complete `Provider` from `@earendil-works/pi-ai`. The provider becomes the composition base and `models.json` overrides still apply above it.
+
 ```typescript
+import { createProvider, openAICompletionsApi } from "@earendil-works/pi-ai";
+
+const provider = createProvider({
+  id: "local-server",
+  name: "Local Server",
+  baseUrl: "http://localhost:8080/v1",
+  auth: {
+    apiKey: {
+      name: "Local server setup",
+      async login(interaction) {
+        return {
+          type: "api_key",
+          key: await interaction.prompt({ type: "secret", message: "API key" }),
+        };
+      },
+      async resolve({ credential }) {
+        return credential?.key
+          ? { auth: { apiKey: credential.key }, source: "stored API key" }
+          : undefined;
+      },
+    },
+  },
+  models: [],
+  api: openAICompletionsApi(),
+});
+
+pi.registerProvider(provider);
+
 // Register a new provider with custom models
 pi.registerProvider("my-proxy", {
   name: "My Proxy",
@@ -1748,7 +1778,9 @@ pi.registerProvider("corporate-ai", {
 });
 ```
 
-**Config options:**
+The object form accepts a complete pi-ai `Provider`, including native `auth`, `getModels`, `refreshModels`, `filterModels`, `stream`, and `streamSimple` behavior.
+
+**Legacy config options:**
 - `name` - Display name for the provider in UI such as `/login`.
 - `baseUrl` - API endpoint URL. Required when defining models.
 - `apiKey` - API key literal, environment interpolation (`$ENV_VAR` or `${ENV_VAR}`), or leading `!command`. Required when defining models (unless `oauth` provided). `$$` escapes `$`, and `$!` escapes a literal `!` without triggering command execution.