[js/rn] Fix React Native CI pipeline E2E test (#16447)

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

Based on this kindly provided quick fix:
https://github.com/microsoft/onnxruntime/pull/16411

See more description in the above linked pr about bumping AGP version,
etc.

Also fixed import header file path in detox e2e test.

### 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. -->

Good build:

https://dev.azure.com/onnxruntime/onnxruntime/_build/results?buildId=1041757&view=logs&j=de302ec2-2305-57e0-e8c6-cd89c569f2a3&t=9894c870-b8ce-548d-51ff-8f44d21a4117&l=18

js/react_native/e2e/android/app/build.gradle

@@ -227,7 +227,7 @@ dependencies {
 // Run this once to be able to run the application with BUCK
 // puts all compile dependencies into folder libs for BUCK to use
 task copyDownloadableDepsToLibs(type: Copy) {
-    from configurations.compile
+    from configurations.implementation
     into 'libs'
 }
 

js/react_native/e2e/android/app/src/main/AndroidManifest.xml

@@ -18,7 +18,8 @@
         android:label="@string/app_name"
         android:configChanges="keyboard|keyboardHidden|orientation|screenSize|uiMode"
         android:launchMode="singleTask"
-        android:windowSoftInputMode="adjustResize">
+        android:windowSoftInputMode="adjustResize"
+        android:exported="true">
         <intent-filter>
             <action android:name="android.intent.action.MAIN" />
             <category android:name="android.intent.category.LAUNCHER" />

js/react_native/e2e/android/build.gradle

@@ -13,7 +13,7 @@ buildscript {
         jcenter()
     }
     dependencies {
-        classpath('com.android.tools.build:gradle:4.1.2')
+        classpath('com.android.tools.build:gradle:7.1.1')
         classpath("org.jetbrains.kotlin:kotlin-gradle-plugin:$kotlinVersion")
         // NOTE: Do not place your application dependencies here; they belong
         // in the individual module build.gradle files

js/react_native/e2e/android/gradle/wrapper/gradle-wrapper.properties

@@ -1,6 +1,6 @@
 distributionBase=GRADLE_USER_HOME
 distributionPath=wrapper/dists
-distributionSha256Sum=7faa7198769f872826c8ef4f1450f839ec27f0b4d5d1e51bade63667cbccd205
-distributionUrl=https\://services.gradle.org/distributions/gradle-6.8.3-bin.zip
+distributionSha256Sum=b586e04868a22fd817c8971330fec37e298f3242eb85c374181b12d637f80302
+distributionUrl=https\://services.gradle.org/distributions/gradle-7.3.3-bin.zip
 zipStoreBase=GRADLE_USER_HOME
 zipStorePath=wrapper/dists

js/react_native/ios/OnnxruntimeModule.mm

@@ -22,7 +22,7 @@
 #include "onnxruntime_extensions.h"
 #else
 #include "onnxruntime/coreml_provider_factory.h"
-#include "onnxruntime/onnxruntime_cxx_api.h"
+#include <onnxruntime/onnxruntime_cxx_api.h>
 #endif
 
 @implementation OnnxruntimeModule

js/react_native/ios/TensorHelper.h

@@ -17,7 +17,7 @@
 #ifdef ORT_ENABLE_EXTENSIONS
 #include "onnxruntime_cxx_api.h"
 #else
-#include "onnxruntime/onnxruntime_cxx_api.h"
+#include <onnxruntime/onnxruntime_cxx_api.h>
 #endif
 
 @interface TensorHelper : NSObject

tools/ci_build/github/azure-pipelines/templates/react-native-ci.yml

@@ -268,9 +268,9 @@ stages:
       displayName: Bootstrap Android and iOS e2e tests
 
     - script: |
-        # Mobile build:
-        # ORT_MOBILE_C_LOCAL_POD_PATH=$(Build.BinariesDirectory)/staging/onnxruntime-mobile-c \
-        ORT_C_LOCAL_POD_PATH=$(Build.BinariesDirectory)/staging/onnxruntime-c \
+        # # Mobile build:
+        # # ORT_MOBILE_C_LOCAL_POD_PATH=$(Build.BinariesDirectory)/staging/onnxruntime-mobile-c \
+        # ORT_C_LOCAL_POD_PATH=$(Build.BinariesDirectory)/staging/onnxruntime-c \
         pod install
       workingDirectory: '$(Build.SourcesDirectory)/js/react_native/e2e/ios'
       displayName: Pod install for onnxruntime react native ios e2e tests