fix (ai/core): forward request headers in generateObject and streamObject (#2299)

Author: lgrammel

.changeset/quiet-socks-eat.md

@@ -0,0 +1,5 @@
+---
+'ai': patch
+---
+
+fix (ai/core): forward request headers in generateObject and streamObject

packages/core/core/generate-object/generate-object.ts

@@ -154,6 +154,7 @@ Default and recommended: 'auto' (best mode for the model).
           inputFormat: validatedPrompt.type,
           prompt: convertToLanguageModelPrompt(validatedPrompt),
           abortSignal,
+          headers,
         }),
       );
 
@@ -193,6 +194,7 @@ Default and recommended: 'auto' (best mode for the model).
           inputFormat: validatedPrompt.type,
           prompt: convertToLanguageModelPrompt(validatedPrompt),
           abortSignal,
+          headers,
         }),
       );