fix(ai): align toolsToModelTools with core AI SDK's prepareToolsAndToolChoice

packages/ai/src/agent/tools-to-model-tools.ts

@@ -1,6 +1,8 @@
 import type { LanguageModelV3FunctionTool } from '@ai-sdk/provider';
 import { asSchema, type ToolSet } from 'ai';
 
+// Mirrors the tool→LanguageModelV3FunctionTool mapping in the core AI SDK's
+// prepareToolsAndToolChoice (ai/src/prompt/prepare-tools-and-tool-choice.ts).
 export async function toolsToModelTools(
   tools: ToolSet
 ): Promise<LanguageModelV3FunctionTool[]> {
@@ -10,6 +12,11 @@ export async function toolsToModelTools(
       name,
       description: tool.description,
       inputSchema: await asSchema(tool.inputSchema).jsonSchema,
+      ...(tool.inputExamples != null
+        ? { inputExamples: tool.inputExamples }
+        : {}),
+      providerOptions: tool.providerOptions,
+      ...(tool.strict != null ? { strict: tool.strict } : {}),
     }))
   );
 }