[js/rn] Fix extensions header include issue (#15800)

### Description
<!-- Describe your changes. -->

Identified the cause for a `redefinition compilation error` happened in
a react native expo app with ort-extensions enabled when running the ios
side. Fix the include path now, so we can remove the temporary forward
declaration in OnnxruntimeModule.mm file.


### Motivation and Context
<!-- - Why is this change required? What problem does it solve?
- If it fixes an open issue, please link to the issue here. -->

Fix implementation detail.

---------

Co-authored-by: rachguo <[email protected]>

Author: 2 people

js/react_native/ios/OnnxruntimeModule.mm

@@ -6,18 +6,19 @@
 
 #import <Foundation/Foundation.h>
 #import <React/RCTLog.h>
-#import <onnxruntime/onnxruntime_cxx_api.h>
 
+// Note: Using below syntax for including ort c api and ort extensions headers to resolve a compiling error happened
+// in an expo react native ios app when ort extensions enabled (a redefinition error of multiple object types defined
+// within ORT C API header). It's an edge case that compiler allows both ort c api headers to be included when #include
+// syntax doesn't match. For the case when extensions not enabled, it still requires a onnxruntime prefix directory for
+// searching paths. Also in general, it's a convention to use #include for C/C++ headers rather then #import. See:
+// https://google.github.io/styleguide/objcguide.html#import-and-include
+// https://microsoft.github.io/objc-guide/Headers/ImportAndInclude.html
 #ifdef ORT_ENABLE_EXTENSIONS
-extern "C" {
-// Note: Declared in onnxruntime_extensions.h but forward declared here to resolve a build issue:
-// (A compilation error happened while building an expo react native ios app, onnxruntime_c_api.h header
-// included in the onnxruntime_extensions.h leads to a redefinition conflicts with multiple object defined in the ORT C
-// API.) So doing a forward declaration here instead of #include "onnxruntime_extensions.h" as a workaround for now
-// before we have a fix.
-// TODO: Investigate if we can include onnxruntime_extensions.h here
-OrtStatus *RegisterCustomOps(OrtSessionOptions *options, const OrtApiBase *api);
-} // Extern C
+#include "onnxruntime_cxx_api.h"
+#include "onnxruntime_extensions.h"
+#else
+#include "onnxruntime/onnxruntime_cxx_api.h"
 #endif
 
 @implementation OnnxruntimeModule

js/react_native/ios/TensorHelper.h

@@ -5,7 +5,19 @@
 #define TensorHelper_h
 
 #import <Foundation/Foundation.h>
-#import <onnxruntime/onnxruntime_cxx_api.h>
+
+// Note: Using below syntax for including ort c api and ort extensions headers to resolve a compiling error happened
+// in an expo react native ios app (a redefinition error happened with multiple object types defined within
+// ORT C API header). It's an edge case that the compiler allows both ort c api headers to be included when #include
+// syntax doesn't match. For the case when extensions not enabled, it still requires a onnxruntime prefix directory for
+// searching paths. Also in general, it's a convention to use #include for C/C++ headers rather then #import. See:
+// https://google.github.io/styleguide/objcguide.html#import-and-include
+// https://microsoft.github.io/objc-guide/Headers/ImportAndInclude.html
+#ifdef ORT_ENABLE_EXTENSIONS
+#include "onnxruntime_cxx_api.h"
+#else
+#include "onnxruntime/onnxruntime_cxx_api.h"
+#endif
 
 @interface TensorHelper : NSObject